lambda  <- c(0.04,-0.191,0.028,0.037,-0.021,0.085,0.015,-0.135,-0.004,0.021,-0.011,0.018,0.022,-0.1,0.047)
year <- as.factor(c(2007,2007,2007,2003,2003,2003,2004,2004,2004,2005,2005,2005,2006,2006,2006))
variable <-as.factor(c("GY","TW","HD","GY","TW","HD","GY","TW","HD","GY","TW","HD","GY","TW","HD"))
tapply(lambda,list(variable),mean)
##      GY      HD      TW 
##  0.0270  0.0348 -0.0916
tapply(lambda,list(variable),sd)
##         GY         HD         TW 
## 0.01088577 0.03355145 0.07634658

Here I use the CPT 2007 data set to illustrate new options avialable for ST Treatment Stability/Trial Dendrogram plots.

Multilocation

Using scripts from ARM ST to show options.

cbPalette <- c("#999999", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
cbbPalette <- c("#000000", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
cbColors <- c(cbPalette,cbbPalette)
path = "../Manuscripts/scripts/multilocation"
means.vector <- read.delim('../Manuscripts/scripts/multilocation/trialMeans.SmyCol1.tab',header=FALSE)
means.matrix <- read.delim('../Manuscripts/scripts/multilocation/trialTable.SmyCol1.tab',header=FALSE)
means.vector <- means.vector[,1]
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 6, 2, 1) + 0.1), ps = 12, cex.lab = 1.166667, cex.main = 1.333333, cex.axis = 1)
res1<-plot.interaction.ARMST(means.matrix, means.vector, ylab='Treatment in Trial Mean \nYield',regression=TRUE, main='Treatment Stability and Trial Clusters for Grand Mean 1', show.legend=TRUE,legend.columns=1, legend.pos=c(.01,.98),trt.colors=cbColors)
par(fig=c(0,1,0,.4),mar=(c(4, 6, 0, 1) + 0.1), new=TRUE)
res2<-plot.clusters.ARMST(means.matrix, means.vector, xlab='Trial Mean \nMultilocation', ylab='',trt.colors =cbColors)

par(fig = c(0, 1, 0, 1))
path = "../Manuscripts/scripts/multilocation"
means.vector <- read.delim('../Manuscripts/scripts/multilocation/trialMeans.SmyCol1.tab',header=FALSE)
means.matrix <- read.delim('../Manuscripts/scripts/multilocation/trialTable.SmyCol1.tab',header=FALSE)
means.vector <- means.vector[,1]
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 6, 2, 1) + 0.1), ps = 12, cex.lab = 1.166667, cex.main = 1.333333, cex.axis = 1)
res1<-plot.interaction.ARMST(means.matrix, means.vector, ylab='Treatment in Trial Mean \nYield',regression=TRUE, main='Treatment Stability and Trial Clusters for Grand Mean 1', show.legend=TRUE,legend.columns=1, legend.pos=c(.01,.98),trt.colors=cbColors)
par(fig=c(0,1,0,.4),mar=(c(4, 6, 0, 1) + 0.1), new=TRUE)
decomp <- decompose.means.table(means.matrix)
fg="black"
res2<-plot.clusters.ARMST(means.matrix, means.vector, fg=fg,xlab='Trial Mean \nMultilocation', ylab='',reference=(decomp$mu + decomp$alpha + decomp$beta),trt.colors=cbColors)
fg=cbColors[2]

res3 <- plot.clusters.ARMST(decomp$mu + decomp$alpha + decomp$beta, means.vector, fg=fg,add=TRUE,xlab='Trial Mean \nMultilocation', ylab='',trt.colors=cbColors)

par(fig = c(0, 1, 0, 1))
str(res2$means.hc)
## List of 7
##  $ merge      : int [1:8, 1:2] -6 -1 -5 -4 2 -2 1 6 -8 -3 ...
##  $ height     : num [1:8] 0.168 0.227 0.385 0.423 0.507 ...
##  $ order      : int [1:9] 2 4 9 6 8 1 3 5 7
##  $ labels     : NULL
##  $ method     : chr "complete"
##  $ call       : language hclust(d = dist(means.matrix), method = method)
##  $ dist.method: chr "euclidean"
##  - attr(*, "class")= chr "hclust"
res2$means.hc$height
## [1] 0.1680609 0.2272786 0.3849098 0.4228869 0.5068531 0.5913357 0.9790983
## [8] 1.9802638
res3$means.hc$height
## [1] 0.05000015 0.05500003 0.10166665 0.12000000 0.42166670 0.44333339
## [7] 0.96833340 1.94666672
res2$means.hc$height/res3$means.hc$height
## [1] 3.361208 4.132335 3.785999 3.524058 1.202023 1.333840 1.011117 1.017259
res2$means.hc$order
## [1] 2 4 9 6 8 1 3 5 7
res3$means.hc$order
## [1] 2 4 9 6 8 5 7 1 3
res2$means.hc$merge
##      [,1] [,2]
## [1,]   -6   -8
## [2,]   -1   -3
## [3,]   -5   -7
## [4,]   -4   -9
## [5,]    2    3
## [6,]   -2    4
## [7,]    1    5
## [8,]    6    7
res3$means.hc$merge
##      [,1] [,2]
## [1,]   -5   -7
## [2,]   -4   -9
## [3,]   -1   -3
## [4,]   -6   -8
## [5,]    1    3
## [6,]   -2    2
## [7,]    4    5
## [8,]    6    7
res2$means.hc$merge==res3$means.hc$merge
##       [,1]  [,2]
## [1,] FALSE FALSE
## [2,] FALSE FALSE
## [3,] FALSE FALSE
## [4,] FALSE FALSE
## [5,] FALSE  TRUE
## [6,]  TRUE FALSE
## [7,] FALSE  TRUE
## [8,]  TRUE  TRUE
matched.idx <- compare.merges(res2$means.hc$merge,res3$means.hc$merge)
matched.idx
## [1] 4 3 1 2 0 0 0 8
res2$means.hc$height
## [1] 0.1680609 0.2272786 0.3849098 0.4228869 0.5068531 0.5913357 0.9790983
## [8] 1.9802638
res3$means.hc$height
## [1] 0.05000015 0.05500003 0.10166665 0.12000000 0.42166670 0.44333339
## [7] 0.96833340 1.94666672
res3$means.hc$height[matched.idx]
## [1] 0.12000000 0.10166665 0.05000015 0.05500003 1.94666672

The function cluster.stats() in the fpc package provides a mechanism for comparing the similarity of two cluster solutions using a variety of validation criteria (Hubert’s gamma coefficient, the Dunn index and the corrected rand index) # comparing 2 cluster solutions

library(fpc)
d <- dist(means.matrix)
cluster.stats(d, res2$clusters, res3$clusters)
## $n
## [1] 9
## 
## $cluster.number
## [1] 3
## 
## $cluster.size
## [1] 4 3 2
## 
## $min.cluster.size
## [1] 2
## 
## $noisen
## [1] 0
## 
## $diameter
## [1] 0.5068531 0.5913357 0.1680609
## 
## $average.distance
## [1] 0.4002332 0.5152329 0.1680609
## 
## $median.distance
## [1] 0.4055768 0.5314759 0.1680609
## 
## $separation
## [1] 0.5229192 0.5952870 0.5229192
## 
## $average.toother
## [1] 0.8850877 1.1943831 1.1381486
## 
## $separation.matrix
##           [,1]     [,2]      [,3]
## [1,] 0.0000000 0.595287 0.5229192
## [2,] 0.5952870 0.000000 1.4083008
## [3,] 0.5229192 1.408301 0.0000000
## 
## $ave.between.matrix
##           [,1]      [,2]      [,3]
## [1,] 0.0000000 0.9694404 0.7585586
## [2,] 0.9694404 0.0000000 1.6442685
## [3,] 0.7585586 1.6442685 0.0000000
## 
## $average.between
## [1] 1.060283
## 
## $average.within
## [1] 0.4115159
## 
## $n.between
## [1] 26
## 
## $n.within
## [1] 10
## 
## $max.diameter
## [1] 0.5913357
## 
## $min.separation
## [1] 0.5229192
## 
## $within.cluster.ss
## [1] 0.5365621
## 
## $clus.avg.silwidths
##         1         2         3 
## 0.4281916 0.4560306 0.7772011 
## 
## $avg.silwidth
## [1] 0.5150289
## 
## $g2
## NULL
## 
## $g3
## NULL
## 
## $pearsongamma
## [1] 0.646884
## 
## $dunn
## [1] 0.8843018
## 
## $dunn2
## [1] 1.472264
## 
## $entropy
## [1] 1.060857
## 
## $wb.ratio
## [1] 0.3881188
## 
## $ch
## [1] 18.8348
## 
## $cwidegap
## [1] 0.3865230 0.5314759 0.1680609
## 
## $widestgap
## [1] 0.5314759
## 
## $sindex
## [1] 0.5229192
## 
## $corrected.rand
## [1] 1
## 
## $vi
## [1] 0

where d is a distance matrix among objects, and fit1\(cluster and fit\)cluster are integer vectors containing classification results from two different clusterings of the same data.

library(SASmixed)
data(Multilocation)
mixed.res <- standard.sensitivity.plot(Multilocation,
                                     response = "Adj",
                          TreatmentName = "Trt",
                          TrialName = "Location",
                          RepName="Block",
                          dual.dendrogram=TRUE,
                          plot.outliers=TRUE,legend.columns=1)
## Loading required package: lme4
## Loading required package: Matrix
## Warning: package 'Matrix' was built under R version 3.3.2
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

print.stdplot(mixed.res)
## [1] ----------------------------------------------------
## [1] Effects
##         [,1]
## 1  0.2822880
## 2 -0.6257370
## 3  0.2254713
## 4 -0.6476620
## 5 -0.1976037
## 6  0.2619546
## 7  0.3421963
## 8  0.5393880
## 9 -0.1802954
##           [,1]
## 1  0.047525000
## 2 -0.086008333
## 3  0.029625000
## 4  0.008858333
## [1] Means
##       [,1]
## 1 2.999675
## 2 2.338883
## 3 2.874392
## 4 2.266025
## 5 2.946042
## 6 3.208492
## 7 3.140733
## 8 3.529417
## 9 2.384083
##       [,1]
## 1 2.924011
## 2 2.677644
## 3 2.949452
## 4 2.865667
## [1] Row Col Means
## [1] 2.999675 2.297058 3.048608 2.550508 2.846858 3.258583 2.842475 3.322483
## [9] 2.521492
##       X1       X2       X3       X4 
## 2.924011 2.677644 2.949452 2.865667 
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
## 
## Response: Adj
##                Df  Sum Sq Mean Sq F value    Pr(>F)    
## Location        8 11.4635 1.43294 41.4400 < 2.2e-16 ***
## Trt             3  1.2217 0.40725 11.7774 4.803e-06 ***
## Location:Trt   24  0.9966 0.04152  1.2008   0.28285    
## Location:Block 18  1.0270 0.05706  1.6500   0.07994 .  
## Residuals      54  1.8672 0.03458                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula: Adj ~ Location + (1 | Location/Block) + (1 | Location:Trt)
##    Data: plot.dat
## 
## REML criterion at convergence: 2.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6168 -0.6321  0.0162  0.5230  2.8392 
## 
## Random effects:
##  Groups         Name        Variance Std.Dev.
##  Location:Trt   (Intercept) 0.015860 0.12594 
##  Block:Location (Intercept) 0.005619 0.07496 
##  Location       (Intercept) 0.028356 0.16839 
##  Residual                   0.034579 0.18595 
## Number of obs: 108, groups:  
## Location:Trt, 36; Block:Location, 27; Location, 9
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  2.99968    0.19255  15.579
## LocationB   -0.70262    0.27231  -2.580
## LocationC    0.04893    0.27231   0.180
## LocationD   -0.44917    0.27231  -1.649
## LocationE   -0.15282    0.27231  -0.561
## LocationF    0.25891    0.27231   0.951
## LocationG   -0.15720    0.27231  -0.577
## LocationH    0.32281    0.27231   1.185
## LocationI   -0.47818    0.27231  -1.756
## 
## Correlation of Fixed Effects:
##           (Intr) LoctnB LoctnC LoctnD LoctnE LoctnF LoctnG LoctnH
## LocationB -0.707                                                 
## LocationC -0.707  0.500                                          
## LocationD -0.707  0.500  0.500                                   
## LocationE -0.707  0.500  0.500  0.500                            
## LocationF -0.707  0.500  0.500  0.500  0.500                     
## LocationG -0.707  0.500  0.500  0.500  0.500  0.500              
## LocationH -0.707  0.500  0.500  0.500  0.500  0.500  0.500       
## LocationI -0.707  0.500  0.500  0.500  0.500  0.500  0.500  0.500
## convergence code: 0
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?
## 
## [1] 
## [1] Stability
## [1] ----------------------------------------------------
##   Treatment     Slope   Intercept     Mean        SD            b
## 1         1 1.0681951 -0.12482441 2.924011 0.3852070  0.068195097
## 2         2 0.9601752 -0.06288138 2.677644 0.3403034 -0.039824803
## 3         3 1.0084981  0.07100300 2.949452 0.3584278  0.008498139
## 4         4 0.9631316  0.11670279 2.865667 0.3556809 -0.036868433
##          Pb         bR2
## 1 0.5890136 0.043775237
## 2 0.6447955 0.032068736
## 3 0.9287174 0.001226858
## 4 0.7959259 0.010207069
## [1] 
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = as.formula(modelString), data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.39512 -0.12950 -0.02166  0.11928  0.57024 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     3.06949    0.06738  45.557  < 2e-16 ***
## Trt2           -0.24637    0.05501  -4.478 2.09e-05 ***
## Trt3            0.02544    0.05501   0.462 0.644817    
## Trt4           -0.05834    0.05501  -1.061 0.291581    
## LocationB      -0.70262    0.08252  -8.515 2.45e-13 ***
## LocationC       0.04893    0.08252   0.593 0.554597    
## LocationD      -0.44917    0.08252  -5.443 4.08e-07 ***
## LocationE      -0.15282    0.08252  -1.852 0.067149 .  
## LocationF       0.25891    0.08252   3.138 0.002269 ** 
## LocationG      -0.15720    0.08252  -1.905 0.059805 .  
## LocationH       0.32281    0.08252   3.912 0.000172 ***
## LocationI      -0.47818    0.08252  -5.795 8.87e-08 ***
## eTrt:eLocation  0.26914    0.56130   0.480 0.632683    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2021 on 95 degrees of freedom
## Multiple R-squared:  0.7658, Adjusted R-squared:  0.7363 
## F-statistic: 25.89 on 12 and 95 DF,  p-value: < 2.2e-16
## 
##                Df Sum Sq Mean Sq F value   Pr(>F)    
## Trt             3  1.222  0.4072   9.968 8.95e-06 ***
## Location        8 11.464  1.4329  35.072  < 2e-16 ***
## eTrt:eLocation  1  0.009  0.0094   0.230    0.633    
## Residuals      95  3.881  0.0409                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] 
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.39061 -0.13704 -0.02025  0.12026  0.58668 
## 
## Coefficients: (1 not defined because of singularities)
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     3.064129   0.069661  43.986  < 2e-16 ***
## Trt2           -0.246367   0.055511  -4.438 2.49e-05 ***
## Trt3            0.025441   0.055511   0.458 0.647807    
## Trt4           -0.058344   0.055511  -1.051 0.295965    
## LocationB      -0.676712   0.110941  -6.100 2.41e-08 ***
## LocationC       0.047129   0.083423   0.565 0.573474    
## LocationD      -0.432607   0.095550  -4.528 1.77e-05 ***
## LocationE      -0.147183   0.084780  -1.736 0.085866 .  
## LocationF       0.249363   0.087540   2.849 0.005406 ** 
## LocationG      -0.151404   0.084867  -1.784 0.077682 .  
## LocationH       0.310907   0.089821   3.461 0.000814 ***
## LocationI      -0.460553   0.097071  -4.745 7.53e-06 ***
## Trt1:eLocation  0.105064   0.170386   0.617 0.538992    
## Trt2:eLocation -0.002956   0.170386  -0.017 0.986194    
## Trt3:eLocation  0.045367   0.170386   0.266 0.790630    
## Trt4:eLocation        NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.204 on 93 degrees of freedom
## Multiple R-squared:  0.7666, Adjusted R-squared:  0.7315 
## F-statistic: 21.82 on 14 and 93 DF,  p-value: < 2.2e-16
## 
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.39061 -0.13704 -0.02025  0.12026  0.58668 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## Trt1            2.92401    0.03785  77.245  < 2e-16 ***
## Trt2            2.67764    0.03785  70.737  < 2e-16 ***
## Trt3            2.94945    0.03785  77.917  < 2e-16 ***
## Trt4            2.86567    0.03785  75.704  < 2e-16 ***
## Trt1:eLocation  1.06820    0.11619   9.194 5.79e-15 ***
## Trt2:eLocation  0.96018    0.11619   8.264 6.13e-13 ***
## Trt3:eLocation  1.00850    0.11619   8.680 7.67e-14 ***
## Trt4:eLocation  0.96313    0.11619   8.289 5.40e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1967 on 100 degrees of freedom
## Multiple R-squared:  0.9957, Adjusted R-squared:  0.9953 
## F-statistic:  2884 on 8 and 100 DF,  p-value: < 2.2e-16
## 
##                Df Sum Sq Mean Sq F value Pr(>F)    
## Trt             4  881.0  220.26 5693.16 <2e-16 ***
## Trt:eLocation   4   11.5    2.87   74.22 <2e-16 ***
## Residuals     100    3.9    0.04                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##               Df Sum Sq Mean Sq F value   Pr(>F)    
## Trt            3  1.222  0.4072   9.790 1.13e-05 ***
## Location       8 11.464  1.4329  34.445  < 2e-16 ***
## Trt:eLocation  3  0.022  0.0073   0.176    0.912    
## Residuals     93  3.869  0.0416                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
##                 Estimate Std. Error     t value  Pr(>|t|)
## Trt1:eLocation 1.0681951  0.1161878  0.58693838 0.2792839
## Trt2:eLocation 0.9601752  0.1161878 -0.34276226 0.3662484
## Trt3:eLocation 1.0084981  0.1161878  0.07314139 0.4709199
## Trt4:eLocation 0.9631316  0.1161878 -0.31731751 0.3758321
## [1] 
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 0.5578604
## [1] Interaction sd Value:
## [1] 0.1201781
## [1] Error sd Value:
## [1] 0.1859535
## [1] Pairs:
## list()
## [1] 
## [1]
response = "Plot.Mean"
TreatmentName = "Criteria.Entry.No."
TrialName = "Expt.No."
RepName="Rep.No."
#yield.desc ="Yield"
#tw.desc="Test Weight"
#hd.desc="Heading"
#ht.desc="Test Weight"
#cpt.dat <- read.csv("CPT.full.subset.csv",header=TRUE)
#cpt.dat <- read.csv("CPT_2007Subsetb.csv",header=TRUE)


yield.desc ="GY"
tw.desc ="TW"
hd.desc="HD"
ht.desc="HT"
cpt.dat <- read.delim("CPT_2007Subset.txt",header=TRUE)
cpt.dat <- subset(cpt.dat,!is.na(cpt.dat$Plot.Mean))
cpt.dat$Expt.No. <- as.factor(cpt.dat$Expt.No.)
TrtNames <- as.character(cpt.dat$Criteria.Entry.No.)
TrtNames[cpt.dat$Criteria.Entry.No.<10] <- paste("0",TrtNames[cpt.dat$Criteria.Entry.No.<10],sep="")
cpt.dat$Criteria.Entry.No. <- as.factor(TrtNames)
cpt.dat$Rep.No. <- as.factor(cpt.dat$Rep.No.)
gy.dat <- subset(cpt.dat,cpt.dat$Description==yield.desc)
tw.dat <- subset(cpt.dat,cpt.dat$Description==tw.desc)
hd.dat <- subset(cpt.dat,cpt.dat$Description==hd.desc)
ht.dat <- subset(cpt.dat,cpt.dat$Description==ht.desc)

gy.dat$Expt.No. <- as.factor(as.character(gy.dat$Expt.No.))
tw.dat$Expt.No. <- as.factor(as.character(tw.dat$Expt.No.))
hd.dat$Expt.No. <- as.factor(as.character(hd.dat$Expt.No.))
ht.dat$Expt.No. <- as.factor(as.character(ht.dat$Expt.No.))
gy.means <- gei.table.and.effects(gy.dat,
                                     response = response,
                          TreatmentName = TreatmentName,
                          TrialName = TrialName,
                          RepName=RepName)
gy.means$trial.means
##        [,1]
## 1  53.67708
## 2  55.57483
## 3  57.78769
## 4  39.01086
## 5  39.54350
## 6  33.59267
## 7  63.30659
## 8  67.83786
## 9  62.65739
## 10 26.95339
## 11 41.62739
## 12 39.34495
## 13 45.65942
colMeans(gy.means$means.table)
##  [1] 53.67708 45.76792 56.31240 52.48333 44.91626 34.96458 55.53854
##  [8] 58.18740 54.31667 30.64583 47.12352 48.92969 43.71042
gy.res <- standard.sensitivity.plot(gy.dat,
                                     response = response,
                          TreatmentName = TreatmentName,
                          TrialName = TrialName,
                          RepName=RepName,
                          dual.dendrogram=FALSE,
                          plot.outliers=TRUE,legend.columns=3)

gy.res <- standard.sensitivity.plot(gy.dat,
                                     response = response,
                          TreatmentName = TreatmentName,
                          TrialName = TrialName,
                          RepName=RepName,
                          outliers=2.4,
                          dual.dendrogram=TRUE,
                          plot.outliers=TRUE,legend.columns=3)

print.stdplot(gy.res)
## [1] ----------------------------------------------------
## [1] Effects
##           [,1]
## 1   -0.8440639
## 2    7.3767696
## 3   15.5864568
## 4   -2.4336466
## 5  -11.9428351
## 6  -20.7732310
## 7   10.5778115
## 8   25.2331226
## 9   15.6730204
## 10 -21.8628136
## 11  -6.7127742
## 12 -10.6329185
## 13   0.7551020
##          [,1]
## 1  -6.1020835
## 2  -2.0020831
## 3   1.0479161
## 4  -2.3020833
## 5  -1.2270835
## 6   4.1979157
## 7   0.4479176
## 8  -1.7020839
## 9  -1.6770833
## 10 -1.4020828
## 11  3.6229178
## 12  7.0979163
## [1] Means
##        [,1]
## 1  53.67708
## 2  55.57483
## 3  57.78769
## 4  39.01086
## 5  39.54350
## 6  33.59267
## 7  63.30659
## 8  67.83786
## 9  62.65739
## 10 26.95339
## 11 41.62739
## 12 39.34495
## 13 45.65942
##        [,1]
## 1  50.43968
## 2  48.36837
## 3  45.21639
## 4  35.26434
## 5  54.32460
## 6  56.79177
## 7  46.15985
## 8  43.17224
## 9  47.68186
## 10 51.02470
## 11 49.67348
## 12 50.25838
## [1] Row Col Means
##  [1] 53.67708 45.76792 56.31240 52.48333 44.91626 34.96458 55.53854
##  [8] 58.18740 54.31667 30.64583 47.12352 48.92969 43.71042
##       X1       X2       X3       X4       X5       X6       X7       X8 
## 50.43968 48.36837 45.21639 35.26434 54.32460 56.79177 46.15985 43.17224 
##       X9      X10      X11      X12 
## 47.68186 51.02470 49.67348 50.25838 
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
## 
## Response: Plot.Mean
##                              Df Sum Sq Mean Sq  F value    Pr(>F)    
## Expt.No.                     12  39698  3308.2 194.3594 < 2.2e-16 ***
## Criteria.Entry.No.           11  17509  1591.7  93.5136 < 2.2e-16 ***
## Expt.No.:Criteria.Entry.No. 132  19964   151.2   8.8856 < 2.2e-16 ***
## Expt.No.:Rep.No.             39   3998   102.5   6.0232 < 2.2e-16 ***
## Residuals                   429   7302    17.0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula: 
## Plot.Mean ~ Expt.No. + (1 | Expt.No./Rep.No.) + (1 | Expt.No.:Criteria.Entry.No.)
##    Data: plot.dat
## 
## REML criterion at convergence: 3977.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.95766 -0.49670 -0.00515  0.49975  2.82744 
## 
## Random effects:
##  Groups                      Name        Variance Std.Dev.
##  Expt.No.:Criteria.Entry.No. (Intercept) 61.256   7.827   
##  Rep.No.:Expt.No.            (Intercept)  7.125   2.669   
##  Expt.No.                    (Intercept) 32.377   5.690   
##  Residual                                17.021   4.126   
## Number of obs: 624, groups:  
## Expt.No.:Criteria.Entry.No., 156; Rep.No.:Expt.No., 52; Expt.No., 13
## 
## Fixed effects:
##                            Estimate Std. Error t value
## (Intercept)                 53.6771     6.2942   8.528
## Expt.No.CPT:2007:Brookings  -7.9092     8.9014  -0.889
## Expt.No.CPT:2007:DLakesPea   2.6353     8.9014   0.296
## Expt.No.CPT:2007:Hayes      -1.1937     8.9014  -0.134
## Expt.No.CPT:2007:Kennebec   -8.7608     8.9014  -0.984
## Expt.No.CPT:2007:Martin    -18.7125     8.9014  -2.102
## Expt.No.CPT:2007:Onida       1.8615     8.9014   0.209
## Expt.No.CPT:2007:Platte      4.5103     8.9014   0.507
## Expt.No.CPT:2007:Selby       0.6396     8.9014   0.072
## Expt.No.CPT:2007:Sturgis   -23.0312     8.9014  -2.587
## Expt.No.CPT:2007:Wall       -6.5536     8.9014  -0.736
## Expt.No.CPT:2007:Watertown  -4.7474     8.9014  -0.533
## Expt.No.CPT:2007:Winner     -9.9667     8.9014  -1.120
## 
## Correlation matrix not shown by default, as p = 13 > 12.
## Use print(summary(fit$lmer), correlation=TRUE)  or
##   vcov(summary(fit$lmer))     if you need it
## [1] 
## [1] Stability
## [1] ----------------------------------------------------
##    Treatment     Slope   Intercept     Mean        SD            b
## 1          1 1.4470667 -19.3059998 50.43968 13.881179  0.447066711
## 2          2 1.1321911  -6.2009466 48.36837 10.210409  0.132191105
## 3          3 0.6213510  15.2685346 45.21639  8.308268 -0.378649035
## 4          4 0.5836777   7.1322629 35.26434  9.429917 -0.416322288
## 5          5 1.2073912  -3.8692090 54.32460 12.212059  0.207391158
## 6          6 1.2629921  -4.0818885 56.79177 12.518736  0.262992078
## 7          7 0.9908940  -1.5992298 46.15985  9.914119 -0.009105978
## 8          8 0.7606544   6.5102431 43.17224  7.677330 -0.239345577
## 9          9 0.9801060   0.4427417 47.68186  8.695932 -0.019894018
## 10        10 1.0053054   2.5710136 51.02470  8.950710  0.005305443
## 11        11 0.9178223   5.4363092 49.67348  8.668054 -0.082177704
## 12        12 1.0905481  -2.3038313 50.25838  9.701141  0.090548106
##           Pb          bR2
## 1  0.1044094 0.2216659526
## 2  0.3810162 0.0703845599
## 3  0.1377338 0.1889368944
## 4  0.1841813 0.1543568700
## 5  0.4304031 0.0574180092
## 6  0.3124248 0.0924748910
## 7  0.9646718 0.0001866071
## 8  0.1593920 0.1715657615
## 9  0.8615537 0.0028891132
## 10 0.9647863 0.0001853985
## 11 0.5949401 0.0265318385
## 12 0.4892785 0.0444565619
## [1] 
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = as.formula(modelString), data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -25.2691  -4.1971   0.0708   4.0414  22.2588 
## 
## Coefficients:
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    55.918792   1.382298  40.454  < 2e-16 ***
## Criteria.Entry.No.02           -2.071312   1.382298  -1.498 0.134542    
## Criteria.Entry.No.03           -5.223290   1.382298  -3.779 0.000173 ***
## Criteria.Entry.No.04          -15.175336   1.382298 -10.978  < 2e-16 ***
## Criteria.Entry.No.05            3.884915   1.382298   2.810 0.005109 ** 
## Criteria.Entry.No.06            6.352087   1.382298   4.595 5.27e-06 ***
## Criteria.Entry.No.07           -4.279829   1.382298  -3.096 0.002052 ** 
## Criteria.Entry.No.08           -7.267437   1.382298  -5.258 2.03e-07 ***
## Criteria.Entry.No.09           -2.757819   1.382298  -1.995 0.046485 *  
## Criteria.Entry.No.10            0.585016   1.382298   0.423 0.672287    
## Criteria.Entry.No.11           -0.766198   1.382298  -0.554 0.579585    
## Criteria.Entry.No.12           -0.181305   1.382298  -0.131 0.895691    
## Expt.No.CPT:2007:Brookings     -7.909166   1.438741  -5.497 5.71e-08 ***
## Expt.No.CPT:2007:DLakesPea      2.635312   1.438741   1.832 0.067496 .  
## Expt.No.CPT:2007:Hayes         -1.193750   1.438741  -0.830 0.407029    
## Expt.No.CPT:2007:Kennebec      -8.760820   1.438741  -6.089 2.03e-09 ***
## Expt.No.CPT:2007:Martin       -18.712500   1.438741 -13.006  < 2e-16 ***
## Expt.No.CPT:2007:Onida          1.861458   1.438741   1.294 0.196230    
## Expt.No.CPT:2007:Platte         4.510312   1.438741   3.135 0.001803 ** 
## Expt.No.CPT:2007:Selby          0.639583   1.438741   0.445 0.656810    
## Expt.No.CPT:2007:Sturgis      -23.031250   1.438741 -16.008  < 2e-16 ***
## Expt.No.CPT:2007:Wall          -6.553567   1.438741  -4.555 6.35e-06 ***
## Expt.No.CPT:2007:Watertown     -4.747396   1.438741  -3.300 0.001025 ** 
## Expt.No.CPT:2007:Winner        -9.966667   1.438741  -6.927 1.11e-11 ***
## eCriteria.Entry.No.:eExpt.No.   0.036771   0.006678   5.506 5.45e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.048 on 599 degrees of freedom
## Multiple R-squared:  0.6636, Adjusted R-squared:  0.6502 
## F-statistic: 49.24 on 24 and 599 DF,  p-value: < 2.2e-16
## 
##                                Df Sum Sq Mean Sq F value   Pr(>F)    
## Criteria.Entry.No.             11  17509    1592   32.04  < 2e-16 ***
## Expt.No.                       12  39698    3308   66.59  < 2e-16 ***
## eCriteria.Entry.No.:eExpt.No.   1   1506    1506   30.32 5.45e-08 ***
## Residuals                     599  29758      50                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] 
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -25.2883  -4.2353   0.1126   4.0307  22.2719 
## 
## Coefficients: (1 not defined because of singularities)
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     56.41492    1.51465  37.246  < 2e-16 ***
## Criteria.Entry.No.02            -2.07131    1.37340  -1.508 0.132048    
## Criteria.Entry.No.03            -5.22329    1.37340  -3.803 0.000158 ***
## Criteria.Entry.No.04           -15.17534    1.37340 -11.049  < 2e-16 ***
## Criteria.Entry.No.05             3.88492    1.37340   2.829 0.004833 ** 
## Criteria.Entry.No.06             6.35209    1.37340   4.625 4.61e-06 ***
## Criteria.Entry.No.07            -4.27983    1.37340  -3.116 0.001921 ** 
## Criteria.Entry.No.08            -7.26744    1.37340  -5.292 1.71e-07 ***
## Criteria.Entry.No.09            -2.75782    1.37340  -2.008 0.045097 *  
## Criteria.Entry.No.10             0.58502    1.37340   0.426 0.670291    
## Criteria.Entry.No.11            -0.76620    1.37340  -0.558 0.577135    
## Criteria.Entry.No.12            -0.18131    1.37340  -0.132 0.895020    
## Expt.No.CPT:2007:Brookings      -8.62533    1.70102  -5.071 5.32e-07 ***
## Expt.No.CPT:2007:DLakesPea       2.87393    1.46212   1.966 0.049814 *  
## Expt.No.CPT:2007:Hayes          -1.30184    1.43624  -0.906 0.365081    
## Expt.No.CPT:2007:Kennebec       -9.55410    1.75681  -5.438 7.89e-08 ***
## Expt.No.CPT:2007:Martin        -20.40688    2.60801  -7.825 2.37e-14 ***
## Expt.No.CPT:2007:Onida           2.03001    1.44585   1.404 0.160840    
## Expt.No.CPT:2007:Platte          4.91871    1.52311   3.229 0.001310 ** 
## Expt.No.CPT:2007:Selby           0.69750    1.43142   0.487 0.626244    
## Expt.No.CPT:2007:Sturgis       -25.11669    3.04164  -8.258 9.81e-16 ***
## Expt.No.CPT:2007:Wall           -7.14698    1.62082  -4.409 1.23e-05 ***
## Expt.No.CPT:2007:Watertown      -5.17726    1.53287  -3.378 0.000780 ***
## Expt.No.CPT:2007:Winner        -10.86913    1.84208  -5.900 6.12e-09 ***
## Criteria.Entry.No.01:eExpt.No.   0.35652    0.17219   2.071 0.038839 *  
## Criteria.Entry.No.02:eExpt.No.   0.04164    0.17219   0.242 0.808984    
## Criteria.Entry.No.03:eExpt.No.  -0.46920    0.17219  -2.725 0.006623 ** 
## Criteria.Entry.No.04:eExpt.No.  -0.50687    0.17219  -2.944 0.003371 ** 
## Criteria.Entry.No.05:eExpt.No.   0.11684    0.17219   0.679 0.497673    
## Criteria.Entry.No.06:eExpt.No.   0.17244    0.17219   1.001 0.317004    
## Criteria.Entry.No.07:eExpt.No.  -0.09965    0.17219  -0.579 0.562979    
## Criteria.Entry.No.08:eExpt.No.  -0.32989    0.17219  -1.916 0.055863 .  
## Criteria.Entry.No.09:eExpt.No.  -0.11044    0.17219  -0.641 0.521511    
## Criteria.Entry.No.10:eExpt.No.  -0.08524    0.17219  -0.495 0.620746    
## Criteria.Entry.No.11:eExpt.No.  -0.17273    0.17219  -1.003 0.316215    
## Criteria.Entry.No.12:eExpt.No.        NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.003 on 589 degrees of freedom
## Multiple R-squared:  0.6735, Adjusted R-squared:  0.6547 
## F-statistic: 35.73 on 34 and 589 DF,  p-value: < 2.2e-16
## 
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -25.2883  -4.2353   0.1126   4.0307  22.2719 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## Criteria.Entry.No.01            50.4397     0.9622  52.421  < 2e-16 ***
## Criteria.Entry.No.02            48.3684     0.9622  50.269  < 2e-16 ***
## Criteria.Entry.No.03            45.2164     0.9622  46.993  < 2e-16 ***
## Criteria.Entry.No.04            35.2643     0.9622  36.650  < 2e-16 ***
## Criteria.Entry.No.05            54.3246     0.9622  56.459  < 2e-16 ***
## Criteria.Entry.No.06            56.7918     0.9622  59.023  < 2e-16 ***
## Criteria.Entry.No.07            46.1599     0.9622  47.973  < 2e-16 ***
## Criteria.Entry.No.08            43.1722     0.9622  44.868  < 2e-16 ***
## Criteria.Entry.No.09            47.6819     0.9622  49.555  < 2e-16 ***
## Criteria.Entry.No.10            51.0247     0.9622  53.029  < 2e-16 ***
## Criteria.Entry.No.11            49.6735     0.9622  51.625  < 2e-16 ***
## Criteria.Entry.No.12            50.2584     0.9622  52.233  < 2e-16 ***
## Criteria.Entry.No.01:eExpt.No.   1.4471     0.1206  11.995  < 2e-16 ***
## Criteria.Entry.No.02:eExpt.No.   1.1322     0.1206   9.385  < 2e-16 ***
## Criteria.Entry.No.03:eExpt.No.   0.6214     0.1206   5.151 3.53e-07 ***
## Criteria.Entry.No.04:eExpt.No.   0.5837     0.1206   4.838 1.67e-06 ***
## Criteria.Entry.No.05:eExpt.No.   1.2074     0.1206  10.009  < 2e-16 ***
## Criteria.Entry.No.06:eExpt.No.   1.2630     0.1206  10.470  < 2e-16 ***
## Criteria.Entry.No.07:eExpt.No.   0.9909     0.1206   8.214 1.32e-15 ***
## Criteria.Entry.No.08:eExpt.No.   0.7607     0.1206   6.305 5.57e-10 ***
## Criteria.Entry.No.09:eExpt.No.   0.9801     0.1206   8.125 2.57e-15 ***
## Criteria.Entry.No.10:eExpt.No.   1.0053     0.1206   8.333 5.36e-16 ***
## Criteria.Entry.No.11:eExpt.No.   0.9178     0.1206   7.608 1.08e-13 ***
## Criteria.Entry.No.12:eExpt.No.   1.0905     0.1206   9.040  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.938 on 600 degrees of freedom
## Multiple R-squared:  0.9812, Adjusted R-squared:  0.9805 
## F-statistic:  1306 on 24 and 600 DF,  p-value: < 2.2e-16
## 
##                               Df  Sum Sq Mean Sq F value Pr(>F)    
## Criteria.Entry.No.            12 1467088  122257 2539.48 <2e-16 ***
## Criteria.Entry.No.:eExpt.No.  12   42077    3506   72.83 <2e-16 ***
## Residuals                    600   28886      48                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##                               Df Sum Sq Mean Sq F value   Pr(>F)    
## Criteria.Entry.No.            11  17509    1592  32.456  < 2e-16 ***
## Expt.No.                      12  39698    3308  67.456  < 2e-16 ***
## Criteria.Entry.No.:eExpt.No.  11   2378     216   4.409 2.19e-06 ***
## Residuals                    589  28886      49                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
##                                 Estimate Std. Error     t value
## Criteria.Entry.No.01:eExpt.No. 1.4470667  0.1206344  3.70596311
## Criteria.Entry.No.02:eExpt.No. 1.1321911  0.1206344  1.09579923
## Criteria.Entry.No.03:eExpt.No. 0.6213510  0.1206344 -3.13881424
## Criteria.Entry.No.04:eExpt.No. 0.5836777  0.1206344 -3.45110697
## Criteria.Entry.No.05:eExpt.No. 1.2073912  0.1206344  1.71917068
## Criteria.Entry.No.06:eExpt.No. 1.2629921  0.1206344  2.18007496
## Criteria.Entry.No.07:eExpt.No. 0.9908940  0.1206344 -0.07548408
## Criteria.Entry.No.08:eExpt.No. 0.7606544  0.1206344 -1.98405710
## Criteria.Entry.No.09:eExpt.No. 0.9801060  0.1206344 -0.16491163
## Criteria.Entry.No.10:eExpt.No. 1.0053054  0.1206344  0.04397952
## Criteria.Entry.No.11:eExpt.No. 0.9178223  0.1206344 -0.68121274
## Criteria.Entry.No.12:eExpt.No. 1.0905481  0.1206344  0.75059926
##                                    Pr(>|t|)
## Criteria.Entry.No.01:eExpt.No. 0.0001150347
## Criteria.Entry.No.02:eExpt.No. 0.1368031433
## Criteria.Entry.No.03:eExpt.No. 0.0008898051
## Criteria.Entry.No.04:eExpt.No. 0.0002987639
## Criteria.Entry.No.05:eExpt.No. 0.0430495326
## Criteria.Entry.No.06:eExpt.No. 0.0148199154
## Criteria.Entry.No.07:eExpt.No. 0.4699273624
## Criteria.Entry.No.08:eExpt.No. 0.0238523464
## Criteria.Entry.No.09:eExpt.No. 0.4345345426
## Criteria.Entry.No.10:eExpt.No. 0.4824676823
## Criteria.Entry.No.11:eExpt.No. 0.2479998550
## Criteria.Entry.No.12:eExpt.No. 0.2265940614
## [1] 
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 9.901533
## [1] Interaction sd Value:
## [1] 6.172434
## [1] Error sd Value:
## [1] 4.125639
## [1] Pairs:
## [[1]]
## [1] 4 1
## 
## [[2]]
## [1] 1 8
## 
## [[3]]
## [1] 4 8
## 
## [[4]]
## [1] 1 9
## 
## [[5]]
## [1] 2 9
## 
## [[6]]
## [1] 3 9
## 
## [[7]]
## [1] 4 9
## 
## [[8]]
## [1] 6 9
## 
## [[9]]
## [1] 7 9
## 
## [[10]]
## [1]  4 10
## 
## [[11]]
## [1]  3 11
## 
## [[12]]
## [1]  4 11
## 
## [[13]]
## [1]  5 11
## 
## [[14]]
## [1]  5 12
## 
## [[15]]
## [1]  6 12
## 
## [[16]]
## [1]  7 12
## 
## [1] 
## [1]
gyb.res <- standard.sensitivity.plot(gy.dat,
                          response = response,
                          TreatmentName = TreatmentName,
                          TrialName = TrialName,
                          RepName=RepName,
                          outliers=2,
                          method="ave",
                          plot.outliers=TRUE,legend.columns=3)

gy2.res <- standard.sensitivity.plot(gy.dat,
                                     response = response,
                          TreatmentName = TreatmentName,
                          TrialName = TrialName,
                          RepName=RepName,
                          outliers=2.4,
                          dual.dendrogram=TRUE,
                          method="ave",
                          plot.outliers=TRUE,legend.columns=3)

means.matrix <- tapply(gy.dat$Plot.Mean,list(gy.dat$Criteria.Entry.No.,gy.dat$Expt.No.),mean)
decomp <- decompose.means.table(means.matrix)
txt.matrix <- decomp$gamma
mean(unlist(txt.matrix),na.rm=TRUE)
## [1] -2.095165e-15
max <- sd(unlist(txt.matrix),na.rm=TRUE)
norm.mat <- abs(txt.matrix)
crit <- 3*max
gy.means$means.table - means.matrix
##    CPT:2007:Bison CPT:2007:Brookings CPT:2007:DLakesPea CPT:2007:Hayes
## 01   5.258016e-13      -1.492140e-13       8.526513e-14  -1.776357e-13
## 02   4.618528e-13      -1.065814e-13       0.000000e+00  -2.131628e-13
## 03   3.055334e-13      -4.973799e-14       1.492140e-13  -1.492140e-13
## 04   6.679102e-13       5.329071e-14       7.105427e-15  -1.563194e-13
## 05  -3.410605e-13      -1.065814e-13      -7.105427e-15  -2.273737e-13
## 06   1.186606e-12      -1.421085e-13       5.684342e-14  -2.344791e-13
## 07   0.000000e+00      -1.421085e-14       0.000000e+00  -2.060574e-13
## 08   4.263256e-14      -5.684342e-14       7.105427e-14  -1.847411e-13
## 09   2.131628e-14      -2.842171e-14       8.526513e-14  -1.634248e-13
## 10   4.192202e-13      -9.237056e-14       4.263256e-14  -1.847411e-13
## 11   1.421085e-13      -8.526513e-14       1.136868e-13  -1.634248e-13
## 12   2.060574e-13      -1.065814e-13       3.552714e-14  -1.918465e-13
##    CPT:2007:Kennebec CPT:2007:Martin CPT:2007:Onida CPT:2007:Platte
## 01      1.705303e-13   -4.725109e-13   1.989520e-13    2.557954e-13
## 02      3.197442e-13   -4.689582e-13   1.989520e-13    2.629008e-13
## 03      3.836931e-13   -4.121148e-13   2.131628e-13    2.273737e-13
## 04      4.369838e-13   -3.907985e-13   2.913225e-13    2.486900e-13
## 05      3.197442e-13   -4.547474e-13   2.060574e-13    2.415845e-13
## 06      3.481659e-13   -4.263256e-13   2.202682e-13    2.415845e-13
## 07      3.836931e-13   -4.547474e-13   2.771117e-13    2.842171e-13
## 08      3.623768e-13   -4.760636e-13   1.918465e-13    2.984279e-13
## 09      4.121148e-13   -4.263256e-13   2.486900e-13    2.984279e-13
## 10      3.979039e-13   -4.547474e-13   2.344791e-13    2.344791e-13
## 11      3.979039e-13   -4.405365e-13   2.202682e-13    2.984279e-13
## 12      3.907985e-13   -4.689582e-13   2.415845e-13    2.984279e-13
##    CPT:2007:Selby CPT:2007:Sturgis CPT:2007:Wall CPT:2007:Watertown
## 01   2.415845e-13     4.263256e-14  1.776357e-13       1.492140e-13
## 02   1.705303e-13    -4.263256e-14  1.421085e-13       1.350031e-13
## 03   3.055334e-13    -2.842171e-14  1.563194e-13       1.847411e-13
## 04   2.167155e-13     1.065814e-14  2.202682e-13       2.273737e-13
## 05   1.847411e-13    -6.394885e-14  1.634248e-13       1.705303e-13
## 06   2.557954e-13    -4.973799e-14  1.918465e-13       1.705303e-13
## 07   2.486900e-13    -3.197442e-14  1.207923e-13       1.350031e-13
## 08   2.060574e-13    -2.486900e-14  1.563194e-13       1.563194e-13
## 09   2.415845e-13    -1.065814e-14  1.989520e-13       2.202682e-13
## 10   2.486900e-13    -2.131628e-14  1.705303e-13       1.918465e-13
## 11   2.273737e-13    -7.105427e-15  1.705303e-13       2.131628e-13
## 12   2.486900e-13    -1.421085e-14  1.918465e-13       1.989520e-13
##    CPT:2007:Winner
## 01    1.421085e-13
## 02    1.492140e-13
## 03    1.563194e-13
## 04    2.060574e-13
## 05    1.421085e-13
## 06    1.705303e-13
## 07    1.421085e-13
## 08    1.705303e-13
## 09    1.847411e-13
## 10    1.634248e-13
## 11    1.918465e-13
## 12    2.060574e-13
gy.res$cluster$score/gy.res$add.cluster$score
##  [1]  1.3927179  1.2256504  1.0296006  1.2545966  0.9612729  0.9204759
##  [7]  0.8777299  0.2101115  0.4671611 77.5177481  0.9335306  0.9547280
gy.res$cluster$clusters
##  [1] 1 1 2 1 1 3 2 2 2 3 1 1 1
gy.res$add.cluster$clusters
##  1  2  3  4  5  6  7  8  9 10 11 12 13 
##  1  2  1  1  2  3  1  1  1  3  2  2  2
gy.res$cluster$means.hc$height
##  [1]  12.75757  16.01341  19.38159  19.76017  23.51187  24.68833  26.87330
##  [8]  34.53185  34.78175  47.55139  62.18434 103.29494
gy.res$add.cluster$means.hc$height
##  [1]  2.215582  2.680709  2.950214  6.256760  6.350852  7.127390  9.175900
##  [8] 14.960588 18.080083 19.759451 50.149726 95.406771
gy.res$cluster$means.hc$height/gy.res$add.cluster$means.hc$height
##  [1] 5.758115 5.973574 6.569555 3.158211 3.702160 3.463867 2.928683
##  [8] 2.308188 1.923760 2.406514 1.239974 1.082679
gy.res$cluster$means.hc$order
##  [1]  6 10  9  8  3  7 11  1  4 12  5  2 13
gy.res$add.cluster$means.hc$order
##  [1]  6 10 11 12 13  2  5  4  1  9  8  3  7
gy.res$cluster$means.hc$merge
##       [,1] [,2]
##  [1,]   -2  -13
##  [2,]   -1   -4
##  [3,]   -3   -7
##  [4,]   -5    1
##  [5,]   -6  -10
##  [6,]   -8    3
##  [7,]  -11    2
##  [8,]   -9    6
##  [9,]  -12    4
## [10,]    7    9
## [11,]    8   10
## [12,]    5   11
gy.res$add.cluster$means.hc$merge
##       [,1] [,2]
##  [1,]   -1   -9
##  [2,]   -3   -7
##  [3,]   -2   -5
##  [4,]  -11  -12
##  [5,]   -4    1
##  [6,]  -13    3
##  [7,]   -8    2
##  [8,]   -6  -10
##  [9,]    4    6
## [10,]    5    7
## [11,]    9   10
## [12,]    8   11
gy.res$cluster$means.hc$merge==gy.res$add.cluster$means.hc$merge
##        [,1]  [,2]
##  [1,] FALSE FALSE
##  [2,] FALSE FALSE
##  [3,] FALSE FALSE
##  [4,] FALSE FALSE
##  [5,] FALSE FALSE
##  [6,] FALSE  TRUE
##  [7,] FALSE  TRUE
##  [8,] FALSE FALSE
##  [9,] FALSE FALSE
## [10,] FALSE FALSE
## [11,] FALSE  TRUE
## [12,] FALSE  TRUE
tdf.tbl <- anova(gy.res$tdf$multiplicative.lm)
aov.tbl <- gy.res$aov
tdf.tbl
## Analysis of Variance Table
## 
## Response: Plot.Mean
##                                Df Sum Sq Mean Sq F value    Pr(>F)    
## Criteria.Entry.No.             11  17509  1591.7  32.039 < 2.2e-16 ***
## Expt.No.                       12  39698  3308.2  66.590 < 2.2e-16 ***
## eCriteria.Entry.No.:eExpt.No.   1   1506  1506.1  30.316 5.451e-08 ***
## Residuals                     599  29758    49.7                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
aov.tbl
## Analysis of Variance Table
## 
## Response: Plot.Mean
##                              Df Sum Sq Mean Sq  F value    Pr(>F)    
## Expt.No.                     12  39698  3308.2 194.3594 < 2.2e-16 ***
## Criteria.Entry.No.           11  17509  1591.7  93.5136 < 2.2e-16 ***
## Expt.No.:Criteria.Entry.No. 132  19964   151.2   8.8856 < 2.2e-16 ***
## Expt.No.:Rep.No.             39   3998   102.5   6.0232 < 2.2e-16 ***
## Residuals                   429   7302    17.0                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
recompute.tdf.aov(tdf.tbl,aov.tbl)
## Analysis of Variance Table
## 
## Response: Plot.Mean
##                                Df Sum Sq Mean Sq F value    Pr(>F)    
## Criteria.Entry.No.             11  17509  1591.7 32.0391 < 2.2e-16 ***
## Expt.No.                       12  39698  3308.2 66.5903 < 2.2e-16 ***
## eCriteria.Entry.No.:eExpt.No.   1   1506  1506.1 22.9645 2.536e-05 ***
## Residuals                      38   2492    65.6  3.8531 3.647e-12 ***
## Residuals1                    429   7302    17.0                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

last = dim(aov.tbl)[1] last.row <- aov.tbl[last,] tdf.last <- dim(tdf.tbl)[1] colnames(last.row) <- colnames(tdf.tbl) tdf.tbl <- rbind(tdf.tbl,last.row) #compute interaction residuals by subtracting 1df row from txt row tdf.tbl[tdf.last,] <- aov.tbl[last-1,] - tdf.tbl[tdf.last-1,] #recompute residuals tdf.tbl[tdf.last,3] <- tdf.tbl[tdf.last,2]/tdf.tbl[tdf.last,1] #test treatment:trial against interaction residual tdf.tbl[tdf.last-1,4] <- tdf.tbl[tdf.last-1,3]/tdf.tbl[tdf.last,3] tdf.tbl[tdf.last-1,5] <- 1-pf(tdf.tbl[tdf.last-1,4],tdf.tbl[tdf.last-1,1],tdf.tbl[tdf.last,1])

#test interaction residual against experimental residual tdf.tbl[tdf.last,4] <- tdf.tbl[tdf.last,3]/last.row[3] tdf.tbl[tdf.last,5] <- 1-pf(tdf.tbl[tdf.last,4],tdf.tbl[tdf.last,1],as.numeric(last.row[1]))

return(tdf.tbl)

```

tw.res <- standard.sensitivity.plot(tw.dat,
                                     response = response,
                          TreatmentName = TreatmentName,
                          TrialName = TrialName,
                          RepName=RepName,
                          dual.dendrogram=TRUE,
                          plot.outliers=TRUE,legend.columns=3)

print.stdplot(tw.res)
## [1] ----------------------------------------------------
## [1] Effects
##          [,1]
## 1   3.8815922
## 2  -0.3701871
## 3  -0.6880950
## 4   5.3024252
## 5  -1.3522327
## 6   2.4545091
## 7  -2.3627820
## 8  -1.6500748
## 9  -4.1854911
## 10  3.8003419
## 11 -1.3228814
## 12 -0.6975722
## 13 -2.8095520
##          [,1]
## 1   0.4520830
## 2  -2.0979172
## 3  -0.2229163
## 4   2.5020831
## 5  -0.2979170
## 6   1.1770833
## 7   2.0270837
## 8  -1.6729161
## 9   0.9770845
## 10 -2.7229163
## 11 -0.2729174
## 12  0.1520828
## [1] Means
##        [,1]
## 1  63.07292
## 2  59.23529
## 3  56.57618
## 4  61.06368
## 5  57.52618
## 6  62.64404
## 7  56.41423
## 8  54.48255
## 9  55.17046
## 10 64.38054
## 11 58.68569
## 12 56.51488
## 13 53.72145
##        [,1]
## 1  59.19784
## 2  59.07935
## 3  57.46056
## 4  57.10709
## 5  60.81155
## 6  60.64901
## 7  59.35348
## 8  55.38728
## 9  60.74249
## 10 57.26328
## 11 57.82618
## 12 56.18782
## [1] Row Col Means
##  [1] 63.07292 57.61053 57.08760 61.85208 53.72670 59.85000 57.23229
##  [8] 55.63458 55.92292 61.14583 58.96981 59.97125 57.41156
##       X1       X2       X3       X4       X5       X6       X7       X8 
## 59.19784 59.07935 57.46056 57.10709 60.81155 60.64901 59.35348 55.38728 
##       X9      X10      X11      X12 
## 60.74249 57.26328 57.82618 56.18782 
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
## 
## Response: Plot.Mean
##                              Df Sum Sq Mean Sq  F value    Pr(>F)    
## Expt.No.                     12 4128.3  344.02 168.3919 < 2.2e-16 ***
## Criteria.Entry.No.           11 1880.3  170.93  83.6688 < 2.2e-16 ***
## Expt.No.:Criteria.Entry.No. 132 1631.9   12.36   6.0515 < 2.2e-16 ***
## Expt.No.:Rep.No.             39  301.6    7.73   3.7854 4.862e-12 ***
## Residuals                   425  868.3    2.04                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula: 
## Plot.Mean ~ Expt.No. + (1 | Expt.No./Rep.No.) + (1 | Expt.No.:Criteria.Entry.No.)
##    Data: plot.dat
## 
## REML criterion at convergence: 2613.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.4708 -0.4532  0.0575  0.5014  2.6909 
## 
## Random effects:
##  Groups                      Name        Variance Std.Dev.
##  Expt.No.:Criteria.Entry.No. (Intercept) 5.6585   2.3788  
##  Rep.No.:Expt.No.            (Intercept) 0.4781   0.6914  
##  Expt.No.                    (Intercept) 7.4666   2.7325  
##  Residual                                2.0446   1.4299  
## Number of obs: 620, groups:  
## Expt.No.:Criteria.Entry.No., 156; Rep.No.:Expt.No., 52; Expt.No., 13
## 
## Fixed effects:
##                            Estimate Std. Error t value
## (Intercept)                  63.073      2.846  22.161
## Expt.No.CPT:2007:Brookings   -5.383      4.026  -1.337
## Expt.No.CPT:2007:DLakesPea   -5.985      4.025  -1.487
## Expt.No.CPT:2007:Hayes       -1.221      4.025  -0.303
## Expt.No.CPT:2007:Kennebec    -9.357      4.025  -2.325
## Expt.No.CPT:2007:Martin      -3.223      4.025  -0.801
## Expt.No.CPT:2007:Onida       -5.841      4.025  -1.451
## Expt.No.CPT:2007:Platte      -7.438      4.025  -1.848
## Expt.No.CPT:2007:Selby       -7.150      4.025  -1.776
## Expt.No.CPT:2007:Sturgis     -1.927      4.025  -0.479
## Expt.No.CPT:2007:Wall        -4.103      4.025  -1.019
## Expt.No.CPT:2007:Watertown   -3.102      4.025  -0.771
## Expt.No.CPT:2007:Winner      -5.661      4.025  -1.407
## 
## Correlation matrix not shown by default, as p = 13 > 12.
## Use print(summary(fit$lmer), correlation=TRUE)  or
##   vcov(summary(fit$lmer))     if you need it
## [1] 
## [1] Stability
## [1] ----------------------------------------------------
##    Treatment     Slope   Intercept     Mean       SD            b
## 1          1 1.0236239  -0.6044865 59.19784 3.206041  0.023623936
## 2          2 0.5756150  25.4506800 59.07935 1.786156 -0.424385033
## 3          3 1.4578990 -27.7130516 57.46056 4.173253  0.457899021
## 4          4 1.6812709 -41.1163899 57.10709 4.908317  0.681270932
## 5          5 0.5923172  26.2070972 60.81155 2.060720 -0.407682801
## 6          6 0.5074963  30.9999788 60.64901 2.078896 -0.492503662
## 7          7 1.0076033   0.4871182 59.35348 3.057007  0.007603260
## 8          8 1.3668135 -24.4649125 55.38728 3.797264  0.366813461
## 9          9 0.5600023  28.0259437 60.74249 1.988947 -0.439997720
## 10        10 1.0024725  -1.3033282 57.26328 2.898771  0.002472472
## 11        11 0.8397078   8.7686355 57.82618 2.473374 -0.160292179
## 12        12 1.3851783 -24.7372847 56.18782 3.860661  0.385178314
##             Pb          bR2
## 1  0.900928919 1.473171e-03
## 2  0.001438911 6.180498e-01
## 3  0.016789197 4.188968e-01
## 4  0.009307985 4.736197e-01
## 5  0.018238667 4.108484e-01
## 6  0.017495975 4.149003e-01
## 7  0.962931685 2.054539e-04
## 8  0.006547976 5.040948e-01
## 9  0.011892635 4.514403e-01
## 10 0.984054800 3.799709e-05
## 11 0.188308310 1.517212e-01
## 12 0.006984747 4.986186e-01
## [1] 
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = as.formula(modelString), data = data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -8.865 -1.207  0.117  1.301  5.082 
## 
## Coefficients:
##                               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                   63.84375    0.39430 161.915  < 2e-16 ***
## Criteria.Entry.No.02          -0.11849    0.39425  -0.301 0.763873    
## Criteria.Entry.No.03          -1.73728    0.39425  -4.407 1.25e-05 ***
## Criteria.Entry.No.04          -1.97890    0.40062  -4.940 1.02e-06 ***
## Criteria.Entry.No.05           1.61371    0.39425   4.093 4.84e-05 ***
## Criteria.Entry.No.06           1.45118    0.39425   3.681 0.000254 ***
## Criteria.Entry.No.07           0.15564    0.39425   0.395 0.693144    
## Criteria.Entry.No.08          -3.81055    0.39425  -9.665  < 2e-16 ***
## Criteria.Entry.No.09           1.54465    0.39425   3.918 9.97e-05 ***
## Criteria.Entry.No.10          -1.93456    0.39425  -4.907 1.20e-06 ***
## Criteria.Entry.No.11          -1.42539    0.39621  -3.598 0.000348 ***
## Criteria.Entry.No.12          -3.01001    0.39425  -7.635 9.05e-14 ***
## Expt.No.CPT:2007:Brookings    -5.34123    0.41753 -12.792  < 2e-16 ***
## Expt.No.CPT:2007:DLakesPea    -5.98531    0.41034 -14.586  < 2e-16 ***
## Expt.No.CPT:2007:Hayes        -1.22083    0.41034  -2.975 0.003047 ** 
## Expt.No.CPT:2007:Kennebec     -9.40444    0.41256 -22.795  < 2e-16 ***
## Expt.No.CPT:2007:Martin       -3.22292    0.41034  -7.854 1.89e-14 ***
## Expt.No.CPT:2007:Onida        -5.84062    0.41034 -14.233  < 2e-16 ***
## Expt.No.CPT:2007:Platte       -7.43833    0.41034 -18.127  < 2e-16 ***
## Expt.No.CPT:2007:Selby        -7.15000    0.41034 -17.424  < 2e-16 ***
## Expt.No.CPT:2007:Sturgis      -1.92708    0.41034  -4.696 3.29e-06 ***
## Expt.No.CPT:2007:Wall         -4.10310    0.41034  -9.999  < 2e-16 ***
## Expt.No.CPT:2007:Watertown    -3.10167    0.41034  -7.559 1.55e-13 ***
## Expt.No.CPT:2007:Winner       -5.66135    0.41034 -13.797  < 2e-16 ***
## eCriteria.Entry.No.:eExpt.No. -0.17781    0.01793  -9.915  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.01 on 595 degrees of freedom
## Multiple R-squared:  0.7271, Adjusted R-squared:  0.7161 
## F-statistic: 66.05 on 24 and 595 DF,  p-value: < 2.2e-16
## 
##                                Df Sum Sq Mean Sq F value Pr(>F)    
## Criteria.Entry.No.             11   1870   170.0   42.06 <2e-16 ***
## Expt.No.                       12   4139   344.9   85.34 <2e-16 ***
## eCriteria.Entry.No.:eExpt.No.   1    397   397.3   98.31 <2e-16 ***
## Residuals                     595   2405     4.0                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] 
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -6.737 -1.138  0.085  1.313  5.415 
## 
## Coefficients: (1 not defined because of singularities)
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     65.62016    0.59968 109.426  < 2e-16 ***
## Criteria.Entry.No.02            -0.11849    0.38063  -0.311 0.755693    
## Criteria.Entry.No.03            -1.73728    0.38063  -4.564 6.11e-06 ***
## Criteria.Entry.No.04            -1.99941    0.38681  -5.169 3.24e-07 ***
## Criteria.Entry.No.05             1.61371    0.38063   4.240 2.60e-05 ***
## Criteria.Entry.No.06             1.45118    0.38063   3.813 0.000152 ***
## Criteria.Entry.No.07             0.15564    0.38063   0.409 0.682757    
## Criteria.Entry.No.08            -3.81055    0.38063 -10.011  < 2e-16 ***
## Criteria.Entry.No.09             1.54465    0.38063   4.058 5.62e-05 ***
## Criteria.Entry.No.10            -1.93456    0.38063  -5.083 5.02e-07 ***
## Criteria.Entry.No.11            -1.40095    0.38265  -3.661 0.000274 ***
## Criteria.Entry.No.12            -3.01001    0.38063  -7.908 1.31e-14 ***
## Expt.No.CPT:2007:Brookings      -7.40290    0.66714 -11.097  < 2e-16 ***
## Expt.No.CPT:2007:DLakesPea      -8.27512    0.71673 -11.546  < 2e-16 ***
## Expt.No.CPT:2007:Hayes          -1.68789    0.41448  -4.072 5.30e-05 ***
## Expt.No.CPT:2007:Kennebec      -12.97131    1.01758 -12.747  < 2e-16 ***
## Expt.No.CPT:2007:Martin         -4.45591    0.51029  -8.732  < 2e-16 ***
## Expt.No.CPT:2007:Onida          -8.07508    0.70475 -11.458  < 2e-16 ***
## Expt.No.CPT:2007:Platte        -10.28402    0.84140 -12.223  < 2e-16 ***
## Expt.No.CPT:2007:Selby          -9.88538    0.81612 -12.113  < 2e-16 ***
## Expt.No.CPT:2007:Sturgis        -2.66433    0.44038  -6.050 2.59e-09 ***
## Expt.No.CPT:2007:Wall           -5.67283    0.56974  -9.957  < 2e-16 ***
## Expt.No.CPT:2007:Watertown      -4.28827    0.50275  -8.530  < 2e-16 ***
## Expt.No.CPT:2007:Winner         -7.82722    0.69002 -11.343  < 2e-16 ***
## Criteria.Entry.No.01:eExpt.No.  -0.36266    0.14736  -2.461 0.014142 *  
## Criteria.Entry.No.02:eExpt.No.  -0.80570    0.14736  -5.468 6.77e-08 ***
## Criteria.Entry.No.03:eExpt.No.   0.07421    0.14736   0.504 0.614739    
## Criteria.Entry.No.04:eExpt.No.   0.28564    0.14753   1.936 0.053331 .  
## Criteria.Entry.No.05:eExpt.No.  -0.78867    0.14736  -5.352 1.25e-07 ***
## Criteria.Entry.No.06:eExpt.No.  -0.87148    0.14736  -5.914 5.68e-09 ***
## Criteria.Entry.No.07:eExpt.No.  -0.37879    0.14736  -2.570 0.010402 *  
## Criteria.Entry.No.08:eExpt.No.  -0.02020    0.14736  -0.137 0.891030    
## Criteria.Entry.No.09:eExpt.No.  -0.81980    0.14736  -5.563 4.03e-08 ***
## Criteria.Entry.No.10:eExpt.No.  -0.37855    0.14736  -2.569 0.010450 *  
## Criteria.Entry.No.11:eExpt.No.  -0.52487    0.14999  -3.499 0.000502 ***
## Criteria.Entry.No.12:eExpt.No.        NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.941 on 585 degrees of freedom
## Multiple R-squared:  0.7499, Adjusted R-squared:  0.7353 
## F-statistic: 51.59 on 34 and 585 DF,  p-value: < 2.2e-16
## 
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.7353 -1.1389  0.0856  1.3044  5.4255 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## Criteria.Entry.No.01            59.1978     0.2667 222.003  < 2e-16 ***
## Criteria.Entry.No.02            59.0793     0.2667 221.558  < 2e-16 ***
## Criteria.Entry.No.03            57.4606     0.2667 215.488  < 2e-16 ***
## Criteria.Entry.No.04            57.2004     0.2747 208.206  < 2e-16 ***
## Criteria.Entry.No.05            60.8115     0.2667 228.054  < 2e-16 ***
## Criteria.Entry.No.06            60.6490     0.2667 227.445  < 2e-16 ***
## Criteria.Entry.No.07            59.3535     0.2667 222.586  < 2e-16 ***
## Criteria.Entry.No.08            55.3873     0.2667 207.712  < 2e-16 ***
## Criteria.Entry.No.09            60.7425     0.2667 227.795  < 2e-16 ***
## Criteria.Entry.No.10            57.2633     0.2667 214.748  < 2e-16 ***
## Criteria.Entry.No.11            57.7966     0.2694 214.507  < 2e-16 ***
## Criteria.Entry.No.12            56.1878     0.2667 210.715  < 2e-16 ***
## Criteria.Entry.No.01:eExpt.No.   1.0194     0.1032   9.874  < 2e-16 ***
## Criteria.Entry.No.02:eExpt.No.   0.5763     0.1032   5.583 3.60e-08 ***
## Criteria.Entry.No.03:eExpt.No.   1.4562     0.1032  14.106  < 2e-16 ***
## Criteria.Entry.No.04:eExpt.No.   1.6675     0.1035  16.117  < 2e-16 ***
## Criteria.Entry.No.05:eExpt.No.   0.5934     0.1032   5.748 1.45e-08 ***
## Criteria.Entry.No.06:eExpt.No.   0.5105     0.1032   4.945 9.89e-07 ***
## Criteria.Entry.No.07:eExpt.No.   1.0032     0.1032   9.718  < 2e-16 ***
## Criteria.Entry.No.08:eExpt.No.   1.3618     0.1032  13.192  < 2e-16 ***
## Criteria.Entry.No.09:eExpt.No.   0.5622     0.1032   5.446 7.54e-08 ***
## Criteria.Entry.No.10:eExpt.No.   1.0035     0.1032   9.720  < 2e-16 ***
## Criteria.Entry.No.11:eExpt.No.   0.8574     0.1068   8.025 5.42e-15 ***
## Criteria.Entry.No.12:eExpt.No.   1.3820     0.1032  13.387  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.923 on 596 degrees of freedom
## Multiple R-squared:  0.999,  Adjusted R-squared:  0.9989 
## F-statistic: 2.394e+04 on 24 and 596 DF,  p-value: < 2.2e-16
## 
##                               Df  Sum Sq Mean Sq F value Pr(>F)    
## Criteria.Entry.No.            12 2119788  176649 47776.3 <2e-16 ***
## Criteria.Entry.No.:eExpt.No.  12    4737     395   106.8 <2e-16 ***
## Residuals                    596    2204       4                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##                               Df Sum Sq Mean Sq F value Pr(>F)    
## Criteria.Entry.No.            11   1870   170.0   45.13 <2e-16 ***
## Expt.No.                      12   4139   344.9   91.56 <2e-16 ***
## Criteria.Entry.No.:eExpt.No.  11    598    54.4   14.44 <2e-16 ***
## Residuals                    585   2204     3.8                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
##                                 Estimate Std. Error     t value
## Criteria.Entry.No.01:eExpt.No. 1.0193656  0.1032350  0.18758810
## Criteria.Entry.No.02:eExpt.No. 0.5763251  0.1032350 -4.10398682
## Criteria.Entry.No.03:eExpt.No. 1.4562332  0.1032350  4.41936798
## Criteria.Entry.No.04:eExpt.No. 1.6674667  0.1034591  6.45150610
## Criteria.Entry.No.05:eExpt.No. 0.5933559  0.1032350 -3.93901529
## Criteria.Entry.No.06:eExpt.No. 0.5105451  0.1032350 -4.74117384
## Criteria.Entry.No.07:eExpt.No. 1.0032367  0.1032350  0.03135295
## Criteria.Entry.No.08:eExpt.No. 1.3618265  0.1032350  3.50488360
## Criteria.Entry.No.09:eExpt.No. 0.5622276  0.1032350 -4.24054415
## Criteria.Entry.No.10:eExpt.No. 1.0034753  0.1032350  0.03366446
## Criteria.Entry.No.11:eExpt.No. 0.8573542  0.1068354 -1.33519302
## Criteria.Entry.No.12:eExpt.No. 1.3820238  0.1032350  3.70052772
##                                    Pr(>|t|)
## Criteria.Entry.No.01:eExpt.No. 4.256317e-01
## Criteria.Entry.No.02:eExpt.No. 2.313376e-05
## Criteria.Entry.No.03:eExpt.No. 5.880879e-06
## Criteria.Entry.No.04:eExpt.No. 1.146625e-10
## Criteria.Entry.No.05:eExpt.No. 4.574919e-05
## Criteria.Entry.No.06:eExpt.No. 1.330452e-06
## Criteria.Entry.No.07:eExpt.No. 4.874993e-01
## Criteria.Entry.No.08:eExpt.No. 2.455515e-04
## Criteria.Entry.No.09:eExpt.No. 1.292144e-05
## Criteria.Entry.No.10:eExpt.No. 4.865780e-01
## Criteria.Entry.No.11:eExpt.No. 9.116146e-02
## Criteria.Entry.No.12:eExpt.No. 1.175387e-04
## [1] 
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 4.287986
## [1] Interaction sd Value:
## [1] 1.769951
## [1] Error sd Value:
## [1] 1.429329
## [1] Pairs:
## [[1]]
## [1] 4 9
## 
## [[2]]
## [1]  4 10
## 
## [1] 
## [1]
tw.res$cluster$score/tw.res$add.cluster$score
##  [1] 1.2259743 0.9697232 0.9300447 0.8278188 0.8531172 0.8305974 0.8721844
##  [8] 3.7475335 1.8639613 0.2142266 1.6386883 0.9722437
tw.res <- standard.sensitivity.plot(tw.dat,
                                     response = response,
                          TreatmentName = TreatmentName,
                          TrialName = TrialName,
                          RepName=RepName,
                          dual.dendrogram=FALSE,
                          plot.outliers=TRUE,legend.columns=3)

gy.matrix <- data.frame(tapply(gy.dat$Plot.Mean,list(gy.dat$Expt.No.,gy.dat$Criteria.Entry.No.),mean))
gy.vector <- tapply(gy.dat$Plot.Mean,list(gy.dat$Expt.No.),mean)

par(fig = c(0, 1, 0.4, 1), mar = (c(1, 4, 1, 1) + 0.1))
gy.table <- plot.interaction.ARMST(gy.matrix, gy.vector, ylab='Treatment in Trial Mean',
                      regression=TRUE, main='GY', show.legend=TRUE,legend.pos=c(.01,.98),
                      legend.columns=4,lwd = 1
                      )
par(fig=c(0,1,0,.4),mar=(c(5, 4, 0, 1) + 0.1), new=TRUE)
gy.hc <- plot.clusters.ARMST(gy.matrix, gy.vector, xlab='Trial Mean', ylab='')

par(fig = c(0, 1, 0, 1))

tw.matrix <- data.frame(tapply(tw.dat$Plot.Mean,list(tw.dat$Expt.No.,tw.dat$Criteria.Entry.No.),mean))
tw.vector <- tapply(tw.dat$Plot.Mean,list(tw.dat$Expt.No.),mean)
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 4, 1, 1) + 0.1))
tw.table <- plot.interaction.ARMST(tw.matrix, tw.vector, ylab='Treatment in Trial Mean',
                      regression=TRUE, main='TW', show.legend=TRUE,legend.pos=c(.01,.98),
                      legend.columns=4,lwd = 1
                      )
par(fig=c(0,1,0,.4),mar=(c(5, 4, 0, 1) + 0.1), new=TRUE)
tw.hc <- plot.clusters.ARMST(tw.matrix, tw.vector, xlab='Trial Mean', ylab='')

par(fig = c(0, 1, 0, 1))

hd.matrix <- data.frame(tapply(hd.dat$Plot.Mean,list(hd.dat$Expt.No.,hd.dat$Criteria.Entry.No.),mean))
hd.vector <- tapply(hd.dat$Plot.Mean,list(hd.dat$Expt.No.),mean)
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 4, 1, 1) + 0.1))
hd.table <- plot.interaction.ARMST(hd.matrix, hd.vector, ylab='Treatment in Trial Mean',
                      regression=TRUE, main='HD', show.legend=TRUE,legend.pos=c(.01,.98),
                      legend.columns=4,lwd = 1
                      )
par(fig=c(0,1,0,.4),mar=(c(5, 4, 0, 1) + 0.1), new=TRUE)
hd.hc <- plot.clusters.ARMST(hd.matrix, hd.vector, xlab='Trial Mean', ylab='')

par(fig = c(0, 1, 0, 1))


ht.matrix <- data.frame(tapply(ht.dat$Plot.Mean,list(ht.dat$Expt.No.,ht.dat$Criteria.Entry.No.),mean))
ht.vector <- tapply(ht.dat$Plot.Mean,list(ht.dat$Expt.No.),mean)
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 4, 1, 1) + 0.1))
ht.table <- plot.interaction.ARMST(ht.matrix, ht.vector, ylab='Treatment in Trial Mean',
                      regression=TRUE, main='HT', show.legend=TRUE,legend.pos=c(.01,.98),
                      legend.columns=4,lwd = 1
                      )
par(fig=c(0,1,0,.4),mar=(c(5, 4, 0, 1) + 0.1), new=TRUE)
ht.hc <- plot.clusters.ARMST(ht.matrix, ht.vector, xlab='Trial Mean', ylab='')

par(fig = c(0, 1, 0, 1))
library(agridat)
data(pacheco.soybean)
mixed.res <- standard.sensitivity.plot(pacheco.soybean,
                                     response = "yield",
                          TreatmentName = "gen",
                          TrialName = "env",
                          dual.dendrogram=TRUE,
                          plot.outliers=TRUE,legend.columns=3)
## Warning in anova.lm(base.lm): ANOVA F-tests on an essentially perfect fit
## are unreliable

print.stdplot(mixed.res)
## [1] ----------------------------------------------------
## [1] Effects
## NULL
## NULL
## [1] Means
##        [,1]
## 1  1756.278
## 2  2222.722
## 3  1910.444
## 4  1234.167
## 5  1682.556
## 6   854.500
## 7  3659.944
## 8  2214.444
## 9  2074.667
## 10 2724.278
## 11 2453.556
##        [,1]
## 1  2457.727
## 2  2053.364
## 3  2181.455
## 4  2172.455
## 5  1736.364
## 6  2173.818
## 7  1860.000
## 8  1858.091
## 9  2053.182
## 10 2225.727
## 11 2258.364
## 12 2081.545
## 13 2085.455
## 14 1920.909
## 15 2159.545
## 16 2117.364
## 17 1922.727
## 18 1970.636
## [1] Row Col Means
##  [1] 1756.278 2289.389 2185.389 1770.944 1659.167 1125.278 2592.500
##  [8] 2400.278 2395.667 2456.778 2155.889
##       X1       X2       X3       X4       X5       X6       X7       X8 
## 2457.727 2053.364 2181.455 2172.455 1736.364 2173.818 1860.000 1858.091 
##       X9      X10      X11      X12      X13      X14      X15      X16 
## 2053.182 2225.727 2258.364 2081.545 2085.455 1920.909 2159.545 2117.364 
##      X17      X18 
## 1922.727 1970.636 
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
## 
## Response: yield
##            Df   Sum Sq Mean Sq F value Pr(>F)
## env        10 35202247 3520225               
## gen        17  5599202  329365               
## env:gen   170 13110345   77120               
## Residuals   0        0                       
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula: yield ~ env + (1 | env)
##    Data: plot.dat
## 
## REML criterion at convergence: 2715.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.4589 -0.5756 -0.1965  0.5819  3.8459 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  env      (Intercept) 271980   521.5   
##  Residual             100051   316.3   
## Number of obs: 198, groups:  env, 11
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  1756.28     526.82   3.334
## envE10        533.11     745.04   0.716
## envE11        429.11     745.04   0.576
## envE2          14.67     745.04   0.020
## envE3         -97.11     745.04  -0.130
## envE4        -631.00     745.04  -0.847
## envE5         836.22     745.04   1.122
## envE6         644.00     745.04   0.864
## envE7         639.39     745.04   0.858
## envE8         700.50     745.04   0.940
## envE9         399.61     745.04   0.536
## 
## Correlation of Fixed Effects:
##        (Intr) envE10 envE11 envE2  envE3  envE4  envE5  envE6  envE7 
## envE10 -0.707                                                        
## envE11 -0.707  0.500                                                 
## envE2  -0.707  0.500  0.500                                          
## envE3  -0.707  0.500  0.500  0.500                                   
## envE4  -0.707  0.500  0.500  0.500  0.500                            
## envE5  -0.707  0.500  0.500  0.500  0.500  0.500                     
## envE6  -0.707  0.500  0.500  0.500  0.500  0.500  0.500              
## envE7  -0.707  0.500  0.500  0.500  0.500  0.500  0.500  0.500       
## envE8  -0.707  0.500  0.500  0.500  0.500  0.500  0.500  0.500  0.500
## envE9  -0.707  0.500  0.500  0.500  0.500  0.500  0.500  0.500  0.500
##        envE8 
## envE10       
## envE11       
## envE2        
## envE3        
## envE4        
## envE5        
## envE6        
## envE7        
## envE8        
## envE9   0.500
## [1] 
## [1] Stability
## [1] ----------------------------------------------------
##    Treatment     Slope    Intercept     Mean       SD           b
## 1          1 1.4371854  -519.540201 2457.727 694.3969  0.43718540
## 2          2 0.7529629   493.528808 2053.364 359.1532 -0.24703714
## 3          3 0.8678092   383.704504 2181.455 416.4498 -0.13219080
## 4          4 0.8428426   426.425245 2172.455 384.2841 -0.15715741
## 5          5 0.8954853  -118.720032 1736.364 466.4005 -0.10451473
## 6          6 0.9302448   246.726824 2173.818 421.7411 -0.06975521
## 7          7 1.0134538  -239.466888 1860.000 496.6359  0.01345384
## 8          8 0.9013210    -9.082115 1858.091 405.0497 -0.09867896
## 9          9 0.9022891   184.003401 2053.182 514.3938 -0.09771092
## 10        10 1.3039264  -475.481353 2225.727 668.1058  0.30392638
## 11        11 1.2222482  -273.640708 2258.364 582.7875  0.22224816
## 12        12 1.6135014 -1260.977590 2081.545 883.7377  0.61350143
## 13        13 0.7168354   600.461273 2085.455 385.8571 -0.28316462
## 14        14 0.6847354   502.414077 1920.909 389.6428 -0.31526464
## 15        15 0.9749964   139.746846 2159.545 493.3809 -0.02500360
## 16        16 0.8326711   392.405551 2117.364 423.7561 -0.16732890
## 17        17 1.1997387  -562.646605 1922.727 581.8160  0.19973872
## 18        18 0.9077530    90.138965 1970.636 446.1592 -0.09224702
##            Pb          bR2
## 1  0.06796959 0.3232929699
## 2  0.03765971 0.3971957795
## 3  0.30632842 0.1155826760
## 4  0.05274230 0.3557873414
## 5  0.58732928 0.0339946462
## 6  0.34517872 0.0993177085
## 7  0.93534335 0.0007726187
## 8  0.10254631 0.2684395841
## 9  0.69896421 0.0174093261
## 10 0.26263331 0.1369371880
## 11 0.20902670 0.1690456689
## 12 0.15294373 0.2130733625
## 13 0.12186434 0.2447356318
## 14 0.12224680 0.2443021526
## 15 0.89303284 0.0021213177
## 16 0.31735312 0.1107330241
## 17 0.29586138 0.1203746658
## 18 0.54524179 0.0420556074
## [1] 
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = as.formula(modelString), data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -646.71 -134.68  -18.94  139.41  859.00 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.142e+03  1.034e+02  20.727  < 2e-16 ***
## genG10      -4.044e+02  1.172e+02  -3.450 0.000708 ***
## genG11      -2.763e+02  1.172e+02  -2.357 0.019556 *  
## genG12      -2.853e+02  1.172e+02  -2.434 0.015972 *  
## genG13      -7.214e+02  1.172e+02  -6.155 5.28e-09 ***
## genG14      -2.839e+02  1.172e+02  -2.422 0.016475 *  
## genG15      -5.977e+02  1.172e+02  -5.100 9.04e-07 ***
## genG16      -5.996e+02  1.172e+02  -5.116 8.39e-07 ***
## genG17      -4.045e+02  1.172e+02  -3.452 0.000704 ***
## genG18      -2.320e+02  1.172e+02  -1.980 0.049383 *  
## genG2       -1.994e+02  1.172e+02  -1.701 0.090775 .  
## genG3       -3.762e+02  1.172e+02  -3.210 0.001590 ** 
## genG4       -3.723e+02  1.172e+02  -3.176 0.001773 ** 
## genG5       -5.368e+02  1.172e+02  -4.580 8.98e-06 ***
## genG6       -2.982e+02  1.172e+02  -2.544 0.011849 *  
## genG7       -3.404e+02  1.172e+02  -2.904 0.004175 ** 
## genG8       -5.350e+02  1.172e+02  -4.565 9.59e-06 ***
## genG9       -4.871e+02  1.172e+02  -4.156 5.14e-05 ***
## envE10       5.331e+02  9.162e+01   5.819 2.90e-08 ***
## envE11       4.291e+02  9.162e+01   4.684 5.77e-06 ***
## envE2        1.467e+01  9.162e+01   0.160 0.873009    
## envE3       -9.711e+01  9.162e+01  -1.060 0.290689    
## envE4       -6.310e+02  9.162e+01  -6.887 1.07e-10 ***
## envE5        8.362e+02  9.162e+01   9.127  < 2e-16 ***
## envE6        6.440e+02  9.162e+01   7.029 4.90e-11 ***
## envE7        6.394e+02  9.162e+01   6.979 6.47e-11 ***
## envE8        7.005e+02  9.162e+01   7.646 1.49e-12 ***
## envE9        3.996e+02  9.162e+01   4.362 2.24e-05 ***
## egen:eenv    5.867e-04  2.755e-04   2.130 0.034651 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 274.9 on 169 degrees of freedom
## Multiple R-squared:  0.7632, Adjusted R-squared:  0.7239 
## F-statistic: 19.45 on 28 and 169 DF,  p-value: < 2.2e-16
## 
##              Df   Sum Sq Mean Sq F value  Pr(>F)    
## gen          17  5599202  329365   4.360 2.2e-07 ***
## env          10 35202247 3520225  46.596 < 2e-16 ***
## egen:eenv     1   342634  342634   4.535  0.0347 *  
## Residuals   169 12767711   75549                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] 
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -701.95 -113.36  -18.73  113.68  832.25 
## 
## Coefficients: (1 not defined because of singularities)
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.171e+03  1.164e+02  18.649  < 2e-16 ***
## genG10      -4.044e+02  1.141e+02  -3.545 0.000522 ***
## genG11      -2.763e+02  1.141e+02  -2.422 0.016611 *  
## genG12      -2.853e+02  1.141e+02  -2.501 0.013447 *  
## genG13      -7.214e+02  1.141e+02  -6.324 2.67e-09 ***
## genG14      -2.839e+02  1.141e+02  -2.489 0.013889 *  
## genG15      -5.977e+02  1.141e+02  -5.240 5.25e-07 ***
## genG16      -5.996e+02  1.141e+02  -5.256 4.86e-07 ***
## genG17      -4.045e+02  1.141e+02  -3.546 0.000519 ***
## genG18      -2.320e+02  1.141e+02  -2.034 0.043706 *  
## genG2       -1.994e+02  1.141e+02  -1.748 0.082531 .  
## genG3       -3.762e+02  1.141e+02  -3.298 0.001212 ** 
## genG4       -3.723e+02  1.141e+02  -3.263 0.001358 ** 
## genG5       -5.368e+02  1.141e+02  -4.706 5.62e-06 ***
## genG6       -2.982e+02  1.141e+02  -2.614 0.009846 ** 
## genG7       -3.404e+02  1.141e+02  -2.984 0.003316 ** 
## genG8       -5.350e+02  1.141e+02  -4.690 6.01e-06 ***
## genG9       -4.871e+02  1.141e+02  -4.270 3.42e-05 ***
## envE10       4.839e+02  1.333e+02   3.630 0.000386 ***
## envE11       3.895e+02  1.197e+02   3.255 0.001394 ** 
## envE2        1.331e+01  8.922e+01   0.149 0.881572    
## envE3       -8.815e+01  9.099e+01  -0.969 0.334144    
## envE4       -5.728e+02  1.474e+02  -3.887 0.000151 ***
## envE5        7.591e+02  1.792e+02   4.235 3.93e-05 ***
## envE6        5.846e+02  1.493e+02   3.916 0.000135 ***
## envE7        5.804e+02  1.486e+02   3.906 0.000141 ***
## envE8        6.359e+02  1.578e+02   4.029 8.81e-05 ***
## envE9        3.627e+02  1.161e+02   3.125 0.002126 ** 
## genG1:eenv   5.294e-01  2.705e-01   1.957 0.052178 .  
## genG10:eenv -1.548e-01  2.705e-01  -0.572 0.568066    
## genG11:eenv -3.994e-02  2.705e-01  -0.148 0.882820    
## genG12:eenv -6.491e-02  2.705e-01  -0.240 0.810710    
## genG13:eenv -1.227e-02  2.705e-01  -0.045 0.963892    
## genG14:eenv  2.249e-02  2.705e-01   0.083 0.933853    
## genG15:eenv  1.057e-01  2.705e-01   0.391 0.696565    
## genG16:eenv -6.432e-03  2.705e-01  -0.024 0.981064    
## genG17:eenv -5.464e-03  2.705e-01  -0.020 0.983913    
## genG18:eenv  3.962e-01  2.705e-01   1.464 0.145149    
## genG2:eenv   3.145e-01  2.705e-01   1.162 0.246862    
## genG3:eenv   7.057e-01  2.705e-01   2.609 0.009992 ** 
## genG4:eenv  -1.909e-01  2.705e-01  -0.706 0.481462    
## genG5:eenv  -2.230e-01  2.705e-01  -0.824 0.411037    
## genG6:eenv   6.724e-02  2.705e-01   0.249 0.804044    
## genG7:eenv  -7.508e-02  2.705e-01  -0.278 0.781755    
## genG8:eenv   2.920e-01  2.705e-01   1.079 0.282175    
## genG9:eenv          NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 267.5 on 153 degrees of freedom
## Multiple R-squared:  0.7969, Adjusted R-squared:  0.7385 
## F-statistic: 13.64 on 44 and 153 DF,  p-value: < 2.2e-16
## 
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -701.95 -113.36  -18.73  113.68  832.25 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## genG1       2457.7273    78.3908  31.352  < 2e-16 ***
## genG10      2053.3636    78.3908  26.194  < 2e-16 ***
## genG11      2181.4545    78.3908  27.828  < 2e-16 ***
## genG12      2172.4545    78.3908  27.713  < 2e-16 ***
## genG13      1736.3636    78.3908  22.150  < 2e-16 ***
## genG14      2173.8182    78.3908  27.731  < 2e-16 ***
## genG15      1860.0000    78.3908  23.727  < 2e-16 ***
## genG16      1858.0909    78.3908  23.703  < 2e-16 ***
## genG17      2053.1818    78.3908  26.192  < 2e-16 ***
## genG18      2225.7273    78.3908  28.393  < 2e-16 ***
## genG2       2258.3636    78.3908  28.809  < 2e-16 ***
## genG3       2081.5455    78.3908  26.553  < 2e-16 ***
## genG4       2085.4545    78.3908  26.603  < 2e-16 ***
## genG5       1920.9091    78.3908  24.504  < 2e-16 ***
## genG6       2159.5455    78.3908  27.548  < 2e-16 ***
## genG7       2117.3636    78.3908  27.010  < 2e-16 ***
## genG8       1922.7273    78.3908  24.527  < 2e-16 ***
## genG9       1970.6364    78.3908  25.139  < 2e-16 ***
## genG1:eenv     1.4372     0.1859   7.730 1.07e-12 ***
## genG10:eenv    0.7530     0.1859   4.050 7.92e-05 ***
## genG11:eenv    0.8678     0.1859   4.668 6.35e-06 ***
## genG12:eenv    0.8428     0.1859   4.534 1.12e-05 ***
## genG13:eenv    0.8955     0.1859   4.817 3.33e-06 ***
## genG14:eenv    0.9302     0.1859   5.004 1.45e-06 ***
## genG15:eenv    1.0135     0.1859   5.451 1.83e-07 ***
## genG16:eenv    0.9013     0.1859   4.848 2.90e-06 ***
## genG17:eenv    0.9023     0.1859   4.853 2.84e-06 ***
## genG18:eenv    1.3039     0.1859   7.014 5.98e-11 ***
## genG2:eenv     1.2222     0.1859   6.574 6.40e-10 ***
## genG3:eenv     1.6135     0.1859   8.679 4.06e-15 ***
## genG4:eenv     0.7168     0.1859   3.856 0.000166 ***
## genG5:eenv     0.6847     0.1859   3.683 0.000314 ***
## genG6:eenv     0.9750     0.1859   5.244 4.84e-07 ***
## genG7:eenv     0.8327     0.1859   4.479 1.41e-05 ***
## genG8:eenv     1.1997     0.1859   6.453 1.21e-09 ***
## genG9:eenv     0.9078     0.1859   4.883 2.49e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 260 on 162 degrees of freedom
## Multiple R-squared:  0.9879, Adjusted R-squared:  0.9852 
## F-statistic: 366.8 on 36 and 162 DF,  p-value: < 2.2e-16
## 
##            Df    Sum Sq  Mean Sq F value Pr(>F)    
## gen        18 855318146 47517675  702.96 <2e-16 ***
## gen:eenv   18  37361982  2075666   30.71 <2e-16 ***
## Residuals 162  10950610    67596                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##              Df   Sum Sq Mean Sq F value   Pr(>F)    
## gen          17  5599202  329365   4.602 9.83e-08 ***
## env          10 35202247 3520225  49.184  < 2e-16 ***
## gen:eenv     17  2159734  127043   1.775   0.0359 *  
## Residuals   153 10950610   71573                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
##              Estimate Std. Error     t value     Pr(>|t|)
## genG1:eenv  1.4371854  0.1859143  2.35154309 0.0099493339
## genG10:eenv 0.7529629  0.1859143 -1.32876913 0.0928963681
## genG11:eenv 0.8678092  0.1859143 -0.71103095 0.2390437689
## genG12:eenv 0.8428426  0.1859143 -0.84532197 0.1995889309
## genG13:eenv 0.8954853  0.1859143 -0.56216628 0.2873898747
## genG14:eenv 0.9302448  0.1859143 -0.37520093 0.3540009053
## genG15:eenv 1.0134538  0.1859143  0.07236585 0.4712000135
## genG16:eenv 0.9013210  0.1859143 -0.53077671 0.2981502055
## genG17:eenv 0.9022891  0.1859143 -0.52556978 0.2999529029
## genG18:eenv 1.3039264  0.1859143  1.63476635 0.0520198576
## genG2:eenv  1.2222482  0.1859143  1.19543360 0.1168323263
## genG3:eenv  1.6135014  0.1859143  3.29991588 0.0005946893
## genG4:eenv  0.7168354  0.1859143 -1.52309251 0.0648426184
## genG5:eenv  0.6847354  0.1859143 -1.69575281 0.0459268312
## genG6:eenv  0.9749964  0.1859143 -0.13448994 0.4465910566
## genG7:eenv  0.8326711  0.1859143 -0.90003261 0.1847194260
## genG8:eenv  1.1997387  0.1859143  1.07435929 0.1421296407
## genG9:eenv  0.9077530  0.1859143 -0.49618045 0.3102198180
## [1] 
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 835.5741
## [1] Interaction sd Value:
## [1] 278.5247
## [1] Error sd Value:
## [1] NaN
## [1] Pairs:
## [[1]]
## [1] 12  3
## 
## [1] 
## [1]
data(cornelius.maize)
mixed.res <- standard.sensitivity.plot(cornelius.maize,
                                     response = "yield",
                          TreatmentName = "gen",
                          TrialName = "env",
                          dual.dendrogram=TRUE,
                          plot.outliers=TRUE,legend.columns=3)
## Warning in anova.lm(base.lm): ANOVA F-tests on an essentially perfect fit
## are unreliable

print.stdplot(mixed.res)
## [1] ----------------------------------------------------
## [1] Effects
## NULL
## NULL
## [1] Means
##        [,1]
## 1  3612.667
## 2  3827.111
## 3  5605.778
## 4  4923.889
## 5  4578.222
## 6  6892.556
## 7  2992.444
## 8  6959.556
## 9  5155.556
## 10 4282.889
## 11 5323.778
## 12 6699.000
## 13 7347.333
## 14 5875.222
## 15 4953.333
## 16 4364.889
## 17 2831.889
## 18 3148.222
## 19 2223.778
## 20 5565.222
##      [,1]
## 1 4617.10
## 2 4603.30
## 3 4822.85
## 4 5217.90
## 5 5247.05
## 6 5330.20
## 7 4672.40
## 8 4283.15
## 9 4929.55
## [1] Row Col Means
##  [1] 3612.667 4209.444 5105.111 5230.111 4955.111 6305.444 3229.444
##  [8] 4027.778 4970.667 2936.444 5307.222 7516.667 6332.333 6052.111
## [15] 5048.889 5406.000 4876.778 4551.444 2652.222 4837.444
##      X1      X2      X3      X4      X5      X6      X7      X8      X9 
## 4617.10 4603.30 4822.85 5217.90 5247.05 5330.20 4672.40 4283.15 4929.55 
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
## 
## Response: yield
##            Df    Sum Sq  Mean Sq F value Pr(>F)
## env        19 247399973 13021051               
## gen         8  19960404  2495051               
## env:gen   152  62420142   410659               
## Residuals   0         0                        
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula: yield ~ env + (1 | env)
##    Data: plot.dat
## 
## REML criterion at convergence: 2602.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.08736 -0.61738 -0.00426  0.64595  2.76388 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  env      (Intercept) 2226600  1492.2  
##  Residual              514878   717.6  
## Number of obs: 180, groups:  env, 20
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)   3612.7     1511.2   2.391
## envE02         596.8     2137.2   0.279
## envE03        1492.4     2137.2   0.698
## envE04        1617.4     2137.2   0.757
## envE05        1342.4     2137.2   0.628
## envE06        2692.8     2137.2   1.260
## envE07        -383.2     2137.2  -0.179
## envE08         415.1     2137.2   0.194
## envE09        1358.0     2137.2   0.635
## envE10        -676.2     2137.2  -0.316
## envE11        1694.6     2137.2   0.793
## envE12        3904.0     2137.2   1.827
## envE13        2719.7     2137.2   1.272
## envE14        2439.4     2137.2   1.141
## envE15        1436.2     2137.2   0.672
## envE16        1793.3     2137.2   0.839
## envE17        1264.1     2137.2   0.592
## envE18         938.8     2137.2   0.439
## envE19        -960.4     2137.2  -0.449
## envE20        1224.8     2137.2   0.573
## 
## Correlation matrix not shown by default, as p = 20 > 12.
## Use print(summary(fit$lmer), correlation=TRUE)  or
##   vcov(summary(fit$lmer))     if you need it
## [1] 
## [1] Stability
## [1] ----------------------------------------------------
##   Treatment     Slope   Intercept    Mean        SD           b
## 1         1 0.9814750  -151.06934 4617.10 1362.2027 -0.01852496
## 2         2 0.9649816   -84.74141 4603.30 1254.0401 -0.03501841
## 3         3 0.9540153   188.08481 4822.85 1206.9871 -0.04598473
## 4         4 1.3142584 -1166.98659 5217.90 1707.5318  0.31425845
## 5         5 1.2280664  -719.10125 5247.05 1565.8725  0.22806640
## 6         6 1.0574596   192.88517 5330.20 1348.6694  0.05745957
## 7         7 0.8575980   506.04604 4672.40 1153.8584 -0.14240201
## 8         8 0.5240001  1737.47020 4283.15  882.0533 -0.47599990
## 9         9 1.1181456  -502.58763 4929.55 1457.8590  0.11814559
##             Pb         bR2
## 1 0.8909193724 0.001073705
## 2 0.7110067554 0.007810197
## 3 0.5384706179 0.021380030
## 4 0.0230407710 0.255349942
## 5 0.0379595028 0.217969243
## 6 0.5214449913 0.023203364
## 7 0.1768890353 0.098897030
## 8 0.0009673339 0.462629361
## 9 0.2980285266 0.059977186
## [1] 
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = as.formula(modelString), data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1706.15  -298.66    -8.26   359.07  2113.48 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.372e+03  2.359e+02  14.293  < 2e-16 ***
## genG2       -1.380e+01  1.891e+02  -0.073 0.941930    
## genG3        2.058e+02  1.891e+02   1.088 0.278384    
## genG4        6.008e+02  1.891e+02   3.177 0.001807 ** 
## genG5        6.300e+02  1.891e+02   3.331 0.001089 ** 
## genG6        7.131e+02  1.891e+02   3.770 0.000233 ***
## genG7        5.530e+01  1.891e+02   0.292 0.770389    
## genG8       -3.339e+02  1.891e+02  -1.766 0.079465 .  
## genG9        3.124e+02  1.891e+02   1.652 0.100605    
## envE02       5.968e+02  2.819e+02   2.117 0.035925 *  
## envE03       1.492e+03  2.819e+02   5.294 4.16e-07 ***
## envE04       1.617e+03  2.819e+02   5.737 5.10e-08 ***
## envE05       1.342e+03  2.819e+02   4.761 4.47e-06 ***
## envE06       2.693e+03  2.819e+02   9.551  < 2e-16 ***
## envE07      -3.832e+02  2.819e+02  -1.359 0.176098    
## envE08       4.151e+02  2.819e+02   1.472 0.143009    
## envE09       1.358e+03  2.819e+02   4.817 3.52e-06 ***
## envE10      -6.762e+02  2.819e+02  -2.398 0.017684 *  
## envE11       1.695e+03  2.819e+02   6.010 1.33e-08 ***
## envE12       3.904e+03  2.819e+02  13.847  < 2e-16 ***
## envE13       2.720e+03  2.819e+02   9.646  < 2e-16 ***
## envE14       2.439e+03  2.819e+02   8.652 6.97e-15 ***
## envE15       1.436e+03  2.819e+02   5.094 1.03e-06 ***
## envE16       1.793e+03  2.819e+02   6.361 2.27e-09 ***
## envE17       1.264e+03  2.819e+02   4.484 1.44e-05 ***
## envE18       9.388e+02  2.819e+02   3.330 0.001093 ** 
## envE19      -9.604e+02  2.819e+02  -3.407 0.000843 ***
## envE20       1.225e+03  2.819e+02   4.344 2.55e-05 ***
## egen:eenv    5.536e-04  1.142e-04   4.848 3.07e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 598.1 on 151 degrees of freedom
## Multiple R-squared:  0.8362, Adjusted R-squared:  0.8058 
## F-statistic: 27.53 on 28 and 151 DF,  p-value: < 2.2e-16
## 
##              Df    Sum Sq  Mean Sq F value   Pr(>F)    
## gen           8  19960404  2495051   6.975 8.28e-08 ***
## env          19 247399973 13021051  36.402  < 2e-16 ***
## egen:eenv     1   8406983  8406983  23.503 3.07e-06 ***
## Residuals   151  54013159   357703                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] 
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1610.55  -334.46    15.47   324.12  2208.91 
## 
## Coefficients: (1 not defined because of singularities)
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.224e+03  2.697e+02  11.956  < 2e-16 ***
## genG2       -1.380e+01  1.880e+02  -0.073 0.941597    
## genG3        2.058e+02  1.880e+02   1.094 0.275688    
## genG4        6.008e+02  1.880e+02   3.195 0.001717 ** 
## genG5        6.300e+02  1.880e+02   3.350 0.001031 ** 
## genG6        7.131e+02  1.880e+02   3.792 0.000219 ***
## genG7        5.530e+01  1.880e+02   0.294 0.769109    
## genG8       -3.339e+02  1.880e+02  -1.776 0.077844 .  
## genG9        3.124e+02  1.880e+02   1.662 0.098756 .  
## envE02       6.673e+02  2.875e+02   2.321 0.021681 *  
## envE03       1.669e+03  3.225e+02   5.174 7.56e-07 ***
## envE04       1.809e+03  3.294e+02   5.491 1.76e-07 ***
## envE05       1.501e+03  3.149e+02   4.766 4.54e-06 ***
## envE06       3.011e+03  4.018e+02   7.493 6.26e-12 ***
## envE07      -4.285e+02  2.833e+02  -1.513 0.132571    
## envE08       4.642e+02  2.838e+02   1.636 0.104126    
## envE09       1.518e+03  3.157e+02   4.810 3.76e-06 ***
## envE10      -7.561e+02  2.895e+02  -2.612 0.009956 ** 
## envE11       1.895e+03  3.338e+02   5.677 7.30e-08 ***
## envE12       4.365e+03  5.028e+02   8.682 7.69e-15 ***
## envE13       3.041e+03  4.039e+02   7.529 5.13e-12 ***
## envE14       2.728e+03  3.829e+02   7.124 4.63e-11 ***
## envE15       1.606e+03  3.196e+02   5.024 1.47e-06 ***
## envE16       2.005e+03  3.396e+02   5.904 2.44e-08 ***
## envE17       1.413e+03  3.112e+02   4.542 1.17e-05 ***
## envE18       1.050e+03  2.977e+02   3.526 0.000567 ***
## envE19      -1.074e+03  2.985e+02  -3.597 0.000441 ***
## envE20       1.369e+03  3.094e+02   4.426 1.88e-05 ***
## genG1:eenv  -1.367e-01  1.604e-01  -0.852 0.395562    
## genG2:eenv  -1.532e-01  1.604e-01  -0.955 0.341201    
## genG3:eenv  -1.641e-01  1.604e-01  -1.023 0.307869    
## genG4:eenv   1.961e-01  1.604e-01   1.223 0.223428    
## genG5:eenv   1.099e-01  1.604e-01   0.685 0.494232    
## genG6:eenv  -6.069e-02  1.604e-01  -0.378 0.705714    
## genG7:eenv  -2.606e-01  1.604e-01  -1.624 0.106461    
## genG8:eenv  -5.941e-01  1.604e-01  -3.704 0.000301 ***
## genG9:eenv          NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 594.6 on 144 degrees of freedom
## Multiple R-squared:  0.8456, Adjusted R-squared:  0.8081 
## F-statistic: 22.53 on 35 and 144 DF,  p-value: < 2.2e-16
## 
## 
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1610.55  -334.46    15.47   324.12  2208.91 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## genG1      4617.1000   125.3564  36.832  < 2e-16 ***
## genG2      4603.3000   125.3564  36.722  < 2e-16 ***
## genG3      4822.8500   125.3564  38.473  < 2e-16 ***
## genG4      5217.9000   125.3564  41.625  < 2e-16 ***
## genG5      5247.0500   125.3564  41.857  < 2e-16 ***
## genG6      5330.2000   125.3564  42.520  < 2e-16 ***
## genG7      4672.4000   125.3564  37.273  < 2e-16 ***
## genG8      4283.1500   125.3564  34.168  < 2e-16 ***
## genG9      4929.5500   125.3564  39.324  < 2e-16 ***
## genG1:eenv    0.9815     0.1069   9.179  < 2e-16 ***
## genG2:eenv    0.9650     0.1069   9.025 5.03e-16 ***
## genG3:eenv    0.9540     0.1069   8.922 9.36e-16 ***
## genG4:eenv    1.3143     0.1069  12.291  < 2e-16 ***
## genG5:eenv    1.2281     0.1069  11.485  < 2e-16 ***
## genG6:eenv    1.0575     0.1069   9.890  < 2e-16 ***
## genG7:eenv    0.8576     0.1069   8.020 2.00e-13 ***
## genG8:eenv    0.5240     0.1069   4.901 2.30e-06 ***
## genG9:eenv    1.1181     0.1069  10.457  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 560.6 on 162 degrees of freedom
## Multiple R-squared:  0.9889, Adjusted R-squared:  0.9876 
## F-statistic: 800.3 on 18 and 162 DF,  p-value: < 2.2e-16
## 
##            Df    Sum Sq   Mean Sq F value Pr(>F)    
## gen         9 4.268e+09 474253490 1508.99 <2e-16 ***
## gen:eenv    9 2.589e+08  28767336   91.53 <2e-16 ***
## Residuals 162 5.091e+07    314285                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##              Df    Sum Sq  Mean Sq F value   Pr(>F)    
## gen           8  19960404  2495051   7.057 7.62e-08 ***
## env          19 247399973 13021051  36.827  < 2e-16 ***
## gen:eenv      8  11506049  1438256   4.068 0.000217 ***
## Residuals   144  50914093   353570                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
##             Estimate Std. Error    t value     Pr(>|t|)
## genG1:eenv 0.9814750  0.1069259 -0.1732504 4.313354e-01
## genG2:eenv 0.9649816  0.1069259 -0.3275016 3.718557e-01
## genG3:eenv 0.9540153  0.1069259 -0.4300616 3.338612e-01
## genG4:eenv 1.3142584  0.1069259  2.9390301 1.886806e-03
## genG5:eenv 1.2280664  0.1069259  2.1329387 1.721801e-02
## genG6:eenv 1.0574596  0.1069259  0.5373775 2.958721e-01
## genG7:eenv 0.8575980  0.1069259 -1.3317822 9.240126e-02
## genG8:eenv 0.5240001  0.1069259 -4.4516800 7.898417e-06
## genG9:eenv 1.1181456  0.1069259  1.1049295 1.354142e-01
## [1] 
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 1928.835
## [1] Interaction sd Value:
## [1] 642.9451
## [1] Error sd Value:
## [1] NaN
## [1] Pairs:
## [[1]]
## [1] 1 8
## 
## [1] 
## [1]
tdf.tbl <- anova(mixed.res$tdf$multiplicative.lm)
anova(mixed.res$tdf$multiplicative.lm)
## Analysis of Variance Table
## 
## Response: yield
##            Df    Sum Sq  Mean Sq F value    Pr(>F)    
## gen         8  19960404  2495051  6.9752 8.283e-08 ***
## env        19 247399973 13021051 36.4018 < 2.2e-16 ***
## egen:eenv   1   8406983  8406983 23.5027 3.070e-06 ***
## Residuals 151  54013159   357703                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(mixed.res$tdf$multiplicative.lm)
## 
## Call:
## lm(formula = as.formula(modelString), data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1706.15  -298.66    -8.26   359.07  2113.48 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.372e+03  2.359e+02  14.293  < 2e-16 ***
## genG2       -1.380e+01  1.891e+02  -0.073 0.941930    
## genG3        2.058e+02  1.891e+02   1.088 0.278384    
## genG4        6.008e+02  1.891e+02   3.177 0.001807 ** 
## genG5        6.300e+02  1.891e+02   3.331 0.001089 ** 
## genG6        7.131e+02  1.891e+02   3.770 0.000233 ***
## genG7        5.530e+01  1.891e+02   0.292 0.770389    
## genG8       -3.339e+02  1.891e+02  -1.766 0.079465 .  
## genG9        3.124e+02  1.891e+02   1.652 0.100605    
## envE02       5.968e+02  2.819e+02   2.117 0.035925 *  
## envE03       1.492e+03  2.819e+02   5.294 4.16e-07 ***
## envE04       1.617e+03  2.819e+02   5.737 5.10e-08 ***
## envE05       1.342e+03  2.819e+02   4.761 4.47e-06 ***
## envE06       2.693e+03  2.819e+02   9.551  < 2e-16 ***
## envE07      -3.832e+02  2.819e+02  -1.359 0.176098    
## envE08       4.151e+02  2.819e+02   1.472 0.143009    
## envE09       1.358e+03  2.819e+02   4.817 3.52e-06 ***
## envE10      -6.762e+02  2.819e+02  -2.398 0.017684 *  
## envE11       1.695e+03  2.819e+02   6.010 1.33e-08 ***
## envE12       3.904e+03  2.819e+02  13.847  < 2e-16 ***
## envE13       2.720e+03  2.819e+02   9.646  < 2e-16 ***
## envE14       2.439e+03  2.819e+02   8.652 6.97e-15 ***
## envE15       1.436e+03  2.819e+02   5.094 1.03e-06 ***
## envE16       1.793e+03  2.819e+02   6.361 2.27e-09 ***
## envE17       1.264e+03  2.819e+02   4.484 1.44e-05 ***
## envE18       9.388e+02  2.819e+02   3.330 0.001093 ** 
## envE19      -9.604e+02  2.819e+02  -3.407 0.000843 ***
## envE20       1.225e+03  2.819e+02   4.344 2.55e-05 ***
## egen:eenv    5.536e-04  1.142e-04   4.848 3.07e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 598.1 on 151 degrees of freedom
## Multiple R-squared:  0.8362, Adjusted R-squared:  0.8058 
## F-statistic: 27.53 on 28 and 151 DF,  p-value: < 2.2e-16

Working backwards, standard error for genotype estimates, the heterogeneous null model, is 560.6/sqrt(20), but I still haven’t worked out the SE for heterogeneous slopes. Still, if we assume balanced, then we can use the given standard error

sqrt(357703)/sqrt(8406983)

ee <- mixed.res\(tdf\)multiplicative.lm\(model\)egenmixed.res\(tdf\)multiplicative.lm\(model\)eenv > sum(eeee) [1] 2.743446e+13 > sqrt(357703/2.743446e+13) [1] 0.0001141861

SE = sb1 = sqrt [ Σ(yi - ŷi)2 / (n - 2) ] / sqrt [ Σ(xi - x)2 ]